Institute of Mathematical Statistics and Actuarial Science

Team

Publications

Books

  1. MOLCHANOV, I.S., Limit Theorems for Unions of Random Closed Sets. Lecture Notes in Mathematics, Springer-Verlag, 1993, 1561..
  2. MOLCHANOV, I.S., Statistics of the Boolean Models for Practitioners and Mathematicians. Wiley, Chichester, 1996.
  3. MOLCHANOV, I. Theory of Random Sets . Springer, London, 2005.
  4. KENDALL, W.S. and MOLCHANOV, I. (Editors) New Perspectives in Stochastic Geometry. Oxford University Press, 2010.
  5. MOLCHANOV, I. Theory of Random Sets . Springer, London, 2017, 2nd edition.
  6. MOLCHANOV, I. and MOLINARI, F. Random Sets in Econometrics. Cambridge University Press, Cambridge, 2018

Articles in refereed scientific journals or refereed proceedings

  1. MOLCHANOV, I., A generalization of the Choquet theorem for random sets with a given class of realizations (Russian). Teor. Veroyatnost. i Matem. Statist., 1983, 28, pp.86-93. English translation in: Theor. Probability and Math. Statist., 1984, 28, pp.99-106.
  2. MOLCHANOV, I., Labelled random sets (Russian). Teor. Veroyatnost. i Matem. Statist., 1983, 29, pp.93-98. English translation in: Theor. Probability and Math. Statist., 1984, 29, pp.113-119.
  3. MOLCHANOV, I., On the structure of strong Markov marked random sets (Russian). Teor. Veroyatnost. i Primen., 1984, 29, n.2, pp.406-407. English translation in: Theory of Probability and Its Applications, 1984, 29, n.2.
  4. MOLCHANOV, I.S., Structure of strong Markov marked random closed sets (Russian). Ukrain. Mat. Zh., 1985, 37, n.1, pp.74-80. English translation in: Ukrainian Math. J., 1985, 37, n.1, pp.63-68.
  5. MOLCHANOV, I.S., Uniform laws of large numbers for empirical associated functionals of random closed sets (Russian). Teor. Veroyatnost. i Primen., 1987, 32, n.3, pp.612-616. English translation in: Theory of Probability and Its Applications, 1987, 32, n.3, pp.556-559. Pdf file.
  6. MOLCHANOV, I.S., Empirical associated functionals and their application to the analysis of stable random sets and processes (Russian). Problems of Stability of Stochastic Models. Eds: V.M.Zolotarev, V.V.Kalashnikov, 1987, pp.75-79. English translation in: J. Soviet Mathematics, 1989, 47, n.5, pp.2742-2746.
  7. MOLCHANOV, I.S., Convergence of empirical accompanying functionals of stationary random sets (Russian). Teor. Veroyatnost. i Matem. Statist., 1988, 38, pp.97-99. English translation in: Theor. Probability and Math. Statist., 1989, 38, pp.107-109. Pdf file.
  8. MOLCHANOV, I.S., A characterization of the universal classes in the Glivenko-Cantelli theorem for random closed sets (Russian). Teor. Veroyatnost. i Matem. Statist., 1989, 41, pp.74--78. English translation in: Theor.  Probability and Math.  Statist., 1990, 41, pp.85--89.
  9. MOLCHANOV, I.S., Estimation of the parameters of superpositions of Poisson point processes (Russian). Teor. Veroyatnost. i Matem. Statist., 1990, 43, pp.111-117. English translation in: Theor. Probability and Math. Statist., 1991, 43, pp.123-130.
  10. MOLCHANOV, I.S., Estimation of the size distribution of spherical grains in the Boolean model. Biometrical J., 1990, 32, n.7, pp.877-886. Pdf file.
  11. MOLCHANOV, I.S., Empirical estimation of distribution quantiles of random closed sets (Russian). Teor. Veroyatnost. i Primen., 1990, 35, n.3, pp.586-592. English translation in: Theory of Probability and Its Applications, 1990, 35, n.3, pp.594-600. Pdf file.
  12. FYODOROV, K.M., GUKALOV, A.V., MOLCHANOV, I.S., Probability methods for the calculation of unit-load conveyer transport systems (Russian). Food Technology, 1990, n.4, pp.79-81.
  13. MOLCHANOV, I.S., Consistent estimation of parameters of Boolean models of random closed sets (Russian). Teor. Veroyatnost. i Primen., 1991, 36, n.3, pp.580-587. English translation in: Theory of Probability and Its Applications, 1991, 36, n.3, pp.600-607. Pdf file.
  14. MOLCHANOV, I.S., On probability metrics in the space of random closed sets distributions (Russian). In: Problems of Stability of Stochastic Models. Eds.: V.M.Zolotarev, V.V.Kalashnikov, 1991, pp.105-111. English translation in: J. of Mathematical Sciences, 1994, 72, n.1, pp.2934-2940.
  15. MOLCHANOV, I.S., Random sets: survey on some results and applications (Russian). Ukrainsk. Matem. Zh., 1991, 43, n.12, pp.1587-1599. English translation in: Ukrainian Math. Journal, 1991, 43, n.12, pp.1477-1487.
  16. MOLCHANOV, I.S., Characterization of random closed sets stable with respect to union (Ukrainian). Teor. Veroyatnost. i Matem. Statist., 1992, 46, pp.114-120. English translation in: Theor. Probability and Math. Statist., 1993, 46, pp.111-116.
  17. MOLCHANOV, I.S., Handling with spatial censored observations in statistics of Boolean models of random sets. Biometrical J., 1992, 34, n.5, pp.617-631.
  18. MOLCHANOV, I.S., On the convergence with probability 1 of random polyhedrons generated by intersections of random half-spaces (Russian). Teor. Veroyatnost. i Primen., 1992, 37, n.4, pp.790-791. English translation in: Theory of Probability and Its Applications, 1992, 37, n.3, p.728.
  19. MOLCHANOV, I.S., Limit theorems for unions of random sets under multiplicative normalization (Russian). Teor. Veroyatnost. i Primen., 1993, 38, n.3, pp.638-645. English translation in: Theory of Probability and Its Applications, 1993, 35, n.3, pp.541-547. Pdf file
  20. MOLCHANOV, I.S., On the convergence of pointwise maxima of special random functions. In: Stability Problems for Stochastic Models. Proceedings of the Fifteenth Perm Seminar, June 1-6, 1992. Eds.: V.M.Zolotarev, V.M.Kruglov, V.Yu.Korolev, 1993, TVP Science Publisher (Ser. Frontiers in Pure and Applied Probability, vol.3, ISBN 90-6764-159-6).
  21. MOLCHANOV, I.S., On regularly varying multivalued functions. In: Stability Problems for Stochastic Models Eds.: V.V.Kalashnikov and V.M.Zolotarev, Lect. Notes Math., 1993, 1546, pp.121-129.
  22. MOLCHANOV, I.S., Limit theorems for convex hulls of random sets. Advances in Applied Probability, 1993, 25, n.2, pp.395-414.
  23. MOLCHANOV, I.S., Intersections and shift functions of strong Markov random closed sets. Probability and Mathematical Statistics, 1993, 14, n.2, pp.265-279.
  24. MOLCHANOV, I.S., Strong law of large numbers for unions of random closed sets. Stochastic Processes and Their Applications, 1993, 46, n.2, pp.199-212.
  25. MOLCHANOV, I.S., STOYAN, D. and FYODOROV, K.M., Directional analysis of planar fibre networks: Application to cardboard microstructure. J. Microscopy, 1993, 172, pp.257-261.
  26. MOLCHANOV, I.S., Statistical analysis of Boolean models with a randomly scaled grain (Ukrainian). Teor. Veroyatnost. i Matem. Statist., 1993, 48, pp.147-154. English translation in: Theor. Probability and Math. Statist., 1994, 48, pp.105-110.
  27. MOLCHANOV, I.S., Generalized expectations of random closed sets. In: Proceedings of the 2nd Ukrainian-Hungarian Conference on Probability Theory Held at Mukachevo, Ukraine, September, 1992. Eds.: A.V.Skorokhod et al., 1993, VSP-TViMC Science Publishers (ISBN 5-85484-02).
  28. MOLCHANOV, I.S., On distributions of random closed sets and expected convex hulls. Statistics and Probability Letters, 1993, 17, pp.253-257.
  29. MOLCHANOV, I.S., A limit theorem for intersections of random half-spaces (Ukrainian). Teor. Veroyatnost. i Matem. Statist., 1993, 49, pp.207-211. English translation in: Theor. Probability and Math. Statist., 1994, 49, pp.147-150.
  30. MOLCHANOV, I.S., On estimation of the shape of an isotropic grain in the Boolean model. Acta Stereologica, 1993, 12/2, Part 1, pp.181-184.
  31. MOLCHANOV, I.S., On statistical analysis of Boolean models with non-random grains. Scand. J. Statist., 1994, 21, pp.73-82.
  32. MOLCHANOV, I.S., STOYAN, D., Asymptotic properties of estimators for parameters of the Boolean model. Advances in Applied Probability, 1994, 26, n.2, pp.301-323.
  33. HEINRICH, L., MOLCHANOV, I.S., Some limit theorems for extremal and union shot-noise processes. Math. Nachrichten, 1994, 168, pp.139-159.
  34. MOLCHANOV, I.S., STOYAN, D., Directional analysis of fibre processes related to Boolean models. Metrika, 1994, 41, pp.183-199.
  35. MOLCHANOV, I.S., Statistics of the Boolean model: from the estimation of means to the estimation of distributions. Adv. Appl. Prob., 1995, 27, 63-86.
  36. MOLCHANOV, I.S., Abstract landmarks and their applications. Proceedings in Current Issues in Statistical Shape Analysis. Eds. K.V.MARDIA and C.A.GILL, Leeds University Press, 1995, 82-87.
  37. MOLCHANOV, I.S., OMEY, E. and KOZAROVITZKY, E., An elementary renewal theorem for random compact convex sets. Adv. Appl. Prob., 1995, 27, 931-942.
  38. MOLCHANOV, I.S. and STOYAN, D., Statistics of compact sets and random polygons. Stochastic Models, 1995, 12, n.2. See also CWI Report BS-R9510.
  39. MOLCHANOV, I.S., Set-valued estimators for mean bodies related to Boolean models. Statistics, 1996, 28, 43-56.
  40. MOLCHANOV, I.S., On the convergence of random processes generated by approximations of convex compact sets. Theory of Probability and its Applications, 1995, 40, 383-390. Pdf file.
  41. MANCHAM, A. and MOLCHANOV, I.S., Stochastic model for randomly perturbed images and related estimation problem. Proceedings in Image Fusion and Shape Variability Techniques. Eds. K.V.MARDIA, C.A.GILL and I.L.DRYDEN, Leeds University Press, 1996, 44-49.
  42. MOLCHANOV, I.S., A limit theorem for scaled vacancies of the Boolean model. Stochastics, Stochastic Reports, 1996, 58, 45-65.
  43. STOYAN, D. and MOLCHANOV, I.S., Set-valued means of random particles. J. of Math. Imaging and Vision, 1997, 7, 111-121.
  44. MOLCHANOV, I.S., Unions of random sets and their applications. Proceedings of International Symposium on Advances in Theory and Applications of Random Sets, Edited by D.~Jeulin, Fontainebleau, 9--11 October 1996, World Scientific Publishing Co., Singapore, 1997, pp. 35-48.
  45. BADDELEY, A.J. and MOLCHANOV, I.S., On the expected measure of a random set. Proceedings of International Symposium on Advances in Theory and Applications of Random Sets, Edited by D.~Jeulin, Fontainebleau, 9--11 October 1996, World Scientific Publishing Co., Singapore, 1997, pp. 3-20.
  46. MOLCHANOV, I.S. Statistical problems for random sets. In: Random Sets: Theory and Applications, IMA Volumes in Mathematics and its Applications, 97, Eds: J.Goutsias, R.P.S.Mahler and H.T.Nguyen, Springer-Verlag, New York, 1997, 27-46.
  47. BADDELEY, A.J. and MOLCHANOV, I.S., Averaging of random sets based on their distance functions. J. Math. Imaging and Vision, 1998, 8, 79-92.
  48. HEIJMANS, H.J.A.M. and MOLCHANOV, I.S. Morphology on convolution lattices with applications to the slope transform and random set theory. Journal of Mathematical Imaging and Vision, 1998, 8, 199-214. Pdf file See also CWI Report BS-R9603 .
  49. MOLCHANOV, I.S. A limit theorem for solutions of inequalities. Scand. J. of Statistics, 1998, 25, 235-242. Pdf file.
  50. KREINOVICH, V. and MOLCHANOV, I.S. How to define an average of several sets? I, II Geocombinatorics, 1998, 7, pp.123--131 and 8, pp.160--165.
  51. CHAPMAN, J.N., ROSE, J., WEIR, I.S., MOLCHANOV, I.S., TITTERINGTON, D.M. The direct observation of magnetisation reversal in films of interest for high density information storage. Proceedings of magneto-Optical Recording International Symposium '97, J. Magn. Soc. Jpn., 22, Suppl. No.S2, 1988, pp.15--20.
  52. MOLCHANOV, I.S. Grey-scale images and random sets. Mathematical Morphology and its Applications to Image and Signal processing, (editors: H.J.A.M.Heijmans, J.B.T.M.Roerdink), 1998, Kluwer, Dordrecht, pp.247--257.
  53. FRIEL, N. and MOLCHANOV, I.S. Distances between grey-scale images. Mathematical Morphology and its Applications to Image and Signal processing, (editors: H.J.A.M.Heijmans, J.B.T.M.Roerdink), 1998, Kluwer, Dordrecht, pp.283--290.
  54. LINDSAY, R., CHAPMAN J.N., CRAVEN A.J., MCBRAIN, D. and MOLCHANOV, I. Grain size distribution and degree of texture in films in integrated circuits. Mat. Res. Soc. Symp. Proc., 523, 1998, pp.85--90.
  55. MOLCHANOV, I.S. Random closed sets: results and problems. In: Stochastic Geometry and Its Applications, Eds: W.S. Kendall, O. Barndorff-Nielsen and M.N.M. van Lieshout}, 1998, pp.285-331, Chapman & Hall, London.
  56. LIESHOUT, M.N.M. van and MOLCHANOV, I.S. Shot-noise-weighted processes: a new family of spatial point processes. Stochastic Models, 14, 1998, pp.715-734. Pdf file
  57. FRIEL, N. and MOLCHANOV, I.S. A class of error metrics for grey-scale image comparison. Mathematical Modeling and Estimation Techniques in Computer Vision (editors: F. Pr{\^e}teux, J. L. Davidson, E. R. Dougherty), 1998, Proceedings of SPIE, 3457, pp.194-201.
  58. MOLCHANOV, I.S. Averaging of random sets and binary images. CWI Quarterly, 11, pp.371-384.
  59. MOLCHANOV, I.S. Random Sets in view of image filtering aplications. In: Nonlinear Filters for Image Processing, Eds: E.R. Dougherty and J.T. Astola, SPIE, 1999, pp.419-447.
  60. WEIR, I.S., CHAPMAN, J.N., MOLCHANOV, I.S., TITTERINGTON, D.M., ROSE, J. Observation and modelling of magnetisation reversal in multilayers supporting perpendicular magnetisation, J. Physics D, 1999, 32, pp.395-403.
  61. HALL, P. and MOLCHANOV, I.S. Corrections for systematic boundary effects in pixel-based area counts. Pattern Recognition, 1999, 32, pp.1519-1528.
  62. FRIEL, N. and MOLCHANOV, I.S. A new thresholding technique based on random sets. Pattern Recognition, 1999, 32, pp.1507-1517.
  63. DOUGHERTY, E.R. and MOLCHANOV, I.S. Special issue on random sets. Introduction. Pattern Recognition, 1999, 32, pp.1473-1474.
  64. MOLCHANOV, I.S. On strong laws of large numbers for random upper semicontinuous functions. J. Math. Analysis and Its Appl., 1999, 235, pp.349-355. Pdf file.
  65. HEINRICH, L. and MOLCHANOV, I.S., Central limit theorem for a class of random measures associated with germ-grain models. Adv. Appl. Probab., 1999, 31, pp.283-314. Pdf file.
  66. MOLCHANOV, I.S., Diffusion limited aggregation with jumps and flights. J. Stat. Comp. Simul., 2000, 64, pp.357-381. Pdf file.
  67. MOLCHANOV, I.S. and CHIU, S.N. Smoothing techniques and estimation methods for non-stationary Boolean models with applications to coverage processes. Biometrika, 2000, 87, pp.265-283. Pdf file Additional numerical results available on request.
  68. MOLCHANOV, I., CHIU, S.N. and ZUYEV, S. Design of inhomogeneous materials with given global properties, Physical Review E, 2000, 62, pp.4544-4552. Additional simulation results and softawre available on request.
  69. MOLCHANOV, I.S. and ZUYEV, S.A. Variational calculus in space of measures and optimal design. In A.C. Atkinson, B. Bogacka, and A. Zhigljavsky, editors, Optimum Experimental Design: Prospects for the New Millennium. Kluwer, Dordrecht, 2000, pp.79-90. Additional numerical results available on request.
  70. MOLCHANOV, I.S. and ZUYEV, S.A. Tangent sets in the space of measures: with applications to variational analysis. J. Math. Anal. Appl., 2000, 249, 539-552. Pdf file
  71. MOLCHANOV, I.S. and ZUYEV, S.A. Variational analysis of functionals of a Poisson process. Mathematics of Operation Research, 2000, 25, pp.485-508. See INRIA Rapport de recherche, No 3302, Nov 1997 for a full variant of this paper.
  72. MOLCHANOV, I.S. and ZUYEV, S.A. Steepest descent algorithms in space of measures. Statistics and Computing, 2002, 12, pp.115-123. Pdf file
  73. VAN LIESHOUT, M.N.M., MOLCHANOV, I.S. and ZUYEV, S.A. Clustering Methods based on Variational Analysis in the Space of Measures. Biometrika, 2001, 88, pp.1021-1033. Pdf file.
  74. MOLCHANOV, I.S. and TERAN, P. Distance transforms for real-valued functions. J. Math. Anal. Appl., 2003, 278, pp.472-484. Pdf file.
  75. CHIU, S.N. and MOLCHANOV, I.S. A new graph related to directional characteristics of point processes. Adv. Appl. Probab., 2003, 35, pp.47-55. Pdf file.
  76. CASCOS, I. and MOLCHANOV, I. A stochastic order for random vectors and random sets based on the Aumann expectation, Statistics and Probability Letters, 2003, 63, pp.295-305. Pdf file.
  77. HALL, P. and MOLCHANOV, I.S. Sequential methods for design-adaptive estimation of discontinuities in regression curves and surfaces, Annals of Statistics , 2003, 31, pp.921-941. See the journal WEB page.
  78. CHIU, S.N., MOLCHANOV, I.S. and QUINE, M.P. Maximum likelihood estimation for germination--growth processes with application to neurotransmitters data. J. Statist. Comput. and Simul. , 2003, 73, pp.725-732. Pdf file
  79. MOLCHANOV, I. and ZUYEV, S. Optimisation in space of measures and optimal design. ESAIM Probability and Statistics, 2004, 8, pp.12-24. Pdf file.
  80. MOLCHANOV, I., SCHERBAKOV, V. Coverage of the whole space. Adv. Appl. Probab., 2003, 35, pp.898-912. Pdf file.
  81. MOLCHANOV, I., SCHERBAKOV, V. and ZUYEV, S. Critical growth of a semi-linear process. J. Appl. Probab., 2004, 41, pp.355-367. Pdf file.
  82. MOLCHANOV, I. Applications of random sets in image analysis. How to average a cat and a dog? In Soft Methodology and Random Information Systems, eds. M. Lopez-Diaz et al., Springer, 2004, pp.8-18. Pdf file.
  83. MRKVICKA, T. and MOLCHANOV, I. Optimisation of linear unbiased intensity estimators for point processes, Ann. Inst. Statist. Math., 2005, 57, pp.71-81. Pdf file
  84. MOLCHANOV, I. Random closed sets. In: Space, Structure, and Randomness, Lect. Notes Stats. 2005, 183, pp.135-149. Pdf file.
  85. MOLCHANOV, I. Stability and stochastic geometry. In: Proceedings S4G. Eds: R.Lechnerov'a, I.Saxl, V.Benes. Prague, Union of Czech Mathematicians and Physisists, 2006, pp. 37--40. Pdf file.
  86. K"OTZER, S. and MOLCHANOV, I. On the domain of attraction for the lower tail in Wicksell's corpuscle problem. In: Proceedings S4G. Eds: R.Lechnerov'a, I.Saxl, V.Benes. Prague, Union of Czech Mathematicians and Physisists, 2006, pp. 91--96. ArXiv math.PR/0607086.
  87. KAVAL, K. and MOLCHANOV, I. Link-save trading. J. Math. Economics 2006, 42, pp.710-728. Pdf file, see also  Economic Working Papers.
  88. MOLCHANOV, I. and TONTCHEV, N. Optimal approximation and quantisation. J. Math. Anal. Appl. 2007, 325, pp.1410-1429. Pdf file.
  89. TER'AN, P. and MOLCHANOV, I. The law of large numbers in a metric space with a convex combination operation, J. Theoret. Probab., 2006, 19, pp.875-898. Pdf file.
  90. HORGAN, G., MOLCHANOV, I. SHCHERBAKOV, V. and ZUYEV, S. Approximate models for bacteria leaching through porous media. Appl. Math. Computation, 2007, 188, pp.1941-1954. Pdf file.
  91. DAVYDOV, Y., MOLCHANOV, I. and ZUYEV, S. Stable distributions and harmonic analysis on convex cones. C.R. Acad. Sci. Paris. Ser. I, 344, 2007, pp.321-326. Pdf file
  92. MOLCHANOV, I. and TONTCHEV, N. Optimal Poisson quantisation. Stat. Probab. Letters, 2007, 77, pp.1123-1132. Pdf file.
  93. CASCOS, I. and MOLCHANOV, I. Multivariate risks and depth-trimmed regions. Finance and Stochastics, 2007, 11, pp.373-397.Pdf file.
  94. MAYER, M. and MOLCHANOV, I. Limit theorems for the diameter of a random sample in the unit ball. Extremes, 2007, 10, pp.129-150. Pdf file. The original publication is available at www.springer.com, DOI.
  95. MOLCHANOV, I. Convex geometry of max-stable distributions. Extremes, 2008, 11, pp.235-259. Pdf file. The original publication is available at www.springer.com, DOI.
  96. DAVYDOV, Y., MOLCHANOV, I. and ZUYEV, S. Strictly stable distributions on convex cones. Electr. J. Probability, 2008, 13, pp.259-321. See EJP WEB site.
  97. MOLCHANOV, I. Convex and star-shaped sets associated with stable distributions. I. Moments and densities. J. Multiv. Analysis, 2009. 100,  pp. 2195-2213. DOI site. Pdf file
  98. MOLCHANOV, I. and SCHMUTZ, M. Multivariate extension of put-call symmetry. SIAM J. Financial Mathematics, 2010, 1, pp.396-426. Pdf file.
  99. DAVYDOV, Y., MOLCHANOV, I. and ZUYEV, S.  Stability for random measures, point processes and discrete semigroups. Bernoulli, 2011, 17, 1015-1043. ArXiv math.PR/0901.0077.
  100. MOLCHANOV, I. Random sets in finance and econometrics. In: New Perspectives in Stochastic Geometry. Eds. W.S. Kendall and I. Molchanov, Oxford University Press, 2010, pp.555-577. Pdf file.
  101. MOLCHANOV, I. and SCHMUTZ, M. Exchangeability-type properties of asset prices. Adv. Appl. Probab. 2011, 43, 666-687. Pdf file.
  102. BERESTEANU, A., MOLCHANOV, I. and MOLINARI, F. Sharp identification regions in models with convex moment predictions. Econometrica, 2011, 79, 1785-1821. Pdf file. Supplement.
  103. KAMPF, J., LAST, G. and MOLCHANOV, I. On the convex hull of   symmetric stable processes. Proc. Amer. Math. Soc., 2012. 140, 2527-2535. Pdf file (pdf, 144KB).
  104. MOLCHANOV, I. and SCHMUTZ, M. Multiasset derivatives and joint distributions of asset prices. Inspired by Finance. The Musiela Festschrift. Eds. Yu. Kabanov, M.~Rutkowski, T.~Zariphopoulou, Springer, 2014, pp.~439--459. Pdf file.
  105. BERESTEANU, A., MOLCHANOV, I. and MOLINARI, F. Partial identification using random sets theory, J. of Econometrics, 2012, 166, 17-32. Cemmap working paper. Pdf file (471KB). Correction (pdf, 78KB).
  106. MOLCHANOV, I. and STUCKI, K. Stationarity of multivariate  particle systems. Stochastic Proc. Appl. 2013, 123, 2272-2285. Arxiv math.
  107. MOLCHANOV, I. , SCHMUTZ, M. and STUCKI, K. Invariance properties of random vectors and stochastic processes based on the zonoid concept. Bernoulli, 2014, 20, 1210-1233. Arxiv math.
  108. CHEVALIER, C., GINSBOURGER, D., BECT, J. and MOLCHANOV, I. Estimating and quantifying uncertainties on level sets using the Vorob’ev expectation and deviation with Gaussian process models. mODa 10 – Advances in Model-Oriented Design and Analysis, Eds. D. Uci{\'n}ski et al. Springer, 2013, 35--43.
  109. CASCOS, I. and MOLCHANOV, I. Choosing a random distribution with prescribed risks. Insur. Math. Econ. 2013, 52, 599-605.
  110. KOPP, C. and MOLCHANOV, I. Large deviations for heavy-tailed random elements in convex cones. J. Math. Anal. Appl. , 2014 411, 271-280, Pdf file.
  111. MOLCHANOV, I. and MOLINARI, F. Applications of random set theory in econometrics. Annual Reviews in Economics, 2014, 6, 229-251.
  112. MOLCHANOV, I. and RALCHENKO K. Multifractional Poisson process, multistable subordinator and related limit theorems. Statist. Probab. Letters}, 2015, 96, 95--101.
  113. LACHIEZE-REY, R. and MOLCHANOV, I. Regularity conditions in the realisability problem in applications to point processes and random closed sets. Annals of Applied Probab., 2015, 25, 116-149.
  114. MOLCHANOV, I. and RALCHENKO K. A generalisation of the fractional Brownian field based on non-Euclidean norms. J. Math. Anal. Appl., 2015}, 430, 262-278.
  115. MOLCHANOV, I. Continued fractions built from convex sets and convex functions. Comm. Contemp. Math., 2015, 17,1550003 (18 pages)
  116. MOLCHANOV, I. and STROKORB, K. Max-stable random sup-measures with comonotonic tail dependence. Stoch. Proc. Appl., 2016, 126, 2835--2859.
  117. MOLCHANOV, I. and WESPI, F. Convex hulls of L\'evy processes. Electr. Comm. Probab., 2016, 21, no. 69, 1-11.
  118. MOLCHANOV, I. and CASCOS, I. Multivariate risk measures: a constructive approach based on selections. Math. Finance, 2016, 26, 867-900.
  119. HAIER, A., MOLCHANOV, I. and SCHMUTZ, M. Intragroup transfers, intragroup diversification and their risk assessment. Ann. Finance, 2016, 12, 363-392.
  120. EVANS, S.N. and MOLCHANOV, I. The semigroup of metric measure spaces and its infinitely divisible measure. Trans. Amer. Math. Soc., 2016, 369, 1797-1834.
  121. MOLCHANOV, I. and ZUYEV, S. Variational analysis of Poisson processes. G. Peccati, M. Reitzner (eds.), Stochastic Analysis for Poisson Point Processes, Bocconi \&\ Springer Series 7, 2016, 81-101.
  122. KOPP, Ch. and MOLCHANOV, I. Series representation of time-stable stochastic processes. Probab. Math. Statist., 2018. In press.
  123. EVANS, S.N. and MOLCHANOV, I. Polar decomposition of scale-homogeneous measures with application to L\'evy measures of strictly stable laws. J. Theor. Probab., 2018.31, 1303-1321.
  124. KLESOV, O. and MOLCHANOV. I. Moment conditions in strong laws of large numbers for multiple sums and random measures. Statist. Probab. Lett., 2017, 131, 56-63.
  125. CASCOS, I. and MOLCHANOV, I. Band depths based on multiple time instances. In: E. Gil, E. Gil, J. Gil, M.-A. Gil. The Mathematics of the Uncertain. A tribute to Pedro Gil, Springer, 2018, 67-78.
  126. ILIENKO, A. and MOLCHANOV, I. Limit theorems for multidimensional renewal sets. Acta Mathematica Hungarica, 2018, 156, 56-81.
  127. DIAYE, M.-A., KOSHEVOY, G.A. and MOLCHANOV, I. Lift expectations of random sets, Statist. Prob. Letters, 2018, 145, 110-117.
  128. KLESOV, O.I. and MOLCHANOV, I. Uniform strong law of large numbers for random signed measures. In: Modern Mathematics and Mechanics. Fundamentals, Problems and Challenges. Eds. Sadovnichiy, V.A. and Zgurovsky, M. Springer, 2019, pp. 335-350.
  129. HAIER, A. and MOLCHANOV, I. Multivariate risk measures in the non-convex setting. Statistics and Risk Analysis , 2019, 36, 25--35.
  130. BOGDANSKII, V.Yu., KLESOV, O.I. and MOLCHANOV,, I. Uniform strong law of large numbers. Methodology and Computing in Applied Probability, 2021, 23, 461-470.
  131. Li, Q. and MOLCHANOV, I. Optimal design for multivariate multiple linear regression with set-identified response. J. Statist. Planning Inference, 2019, 203, 215-223.
  132. LEPINETTE, E. and MOLCHANOV, I. Conditional cores and conditional convex hulls of random sets. J. Math. Anal. Appl., 2019, 478, 368-392.
  133. MOLCHANOV, I. and NAGEL, F. Diagonal Minkowski classes, zonoid equivalence, and stable laws. Comm. Contemp. Math., 2019, 1950091.
  134. ARNOLD, S., MOLCHANOV, I. and ZIEGEL, J. F. Bivariate distributions with ordered marginals. J. Multiv. Anal., 2020, 104585.
  135. BHATTACHARJEE, C. and MOLCHANOV, I. Convergence to scale-invariant Poisson processes and applications in Dickman approximation. Electron. J. Probability, 2020, 25, 1-20.
  136. LI, Q., MOLCHANOV,, I., MOLINARI, F. and PENG, S. Local regression smoothers with set-valued outcome data. Intern. J. Approx. Reasoning, 2021, 128, 129-150.
  137. MARYNYCH, A. and MOLCHANOV, I. Sieving random iterative function systems. Bernoulli, 2021, 27(1), 34-65.
  138. MOLCHANOV, I., M"UHLEMANN, A. Nonlinear expectations of random sets. Finance and Stochastics, 2021, 25, 5-41.
  139. LEPINETTE, E. and MOLCHANOV, I. Risk arbitrage and hedging to acceptability under transaction costs. Finance and Stochastics, 2021, 25, 101-132.
  140. CASCOS, I., Ii, Q. and MOLCHANOV, I. Depth and outliers for samples of sets and random sets distributions. ustralian and New Zealand J. Statist., 2021, 63, 55-82.
  141. MOLCHANOV,, I., TYRIN, R. Convex bodies generated by sublinear expectations of random vectors. Advances in Applied Math., 2021, Paper No, 102251, 31 pp.
  142. MARYNYCH, A. and MOLCHANOV, I. Facial structure of strongly convex sets generated by random samples. dvances in Math., 2022, 395, 108086.
  143. BHATTACHARJEE, C. and MOLCHANOV, I. Gaussian approximation for sums of region-stabilizing scores. Electr. J. Probab., 27, Paper No. 111: 1-27, 2022.

Some other publications

  1. DALEY, D., KENDALL, W.S., MOLCHANOV, I. and VEDEL JENSEN E. Dietrich Stoyan: A tribute on the occasion of his seventieth birthday, Adv. Appl. Prob., 2010, 43.
  2. MOLCHANOV I. Foundations of stochastic geometry and theory of random sets. In: Stochastic Geometry, Spatial Statistics and Random Fields,  Ed. E.Spodarev, 2013, Lect. Notes. Math., 2068, 1--20. Springer, Heidelberg.