V. I. Bogachev, A. V. Kolesnikov, “Open Mappings of Probability Measures and the Skorokhod Representation Theorem”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 3–27; Theory Probab. Appl., 46:1 (2002), 20

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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 1, Pages 3–27
DOI: https://doi.org/10.4213/tvp3944 (Mi tvp3944)

This article is cited in 11 scientific papers (total in 12 papers)

Open Mappings of Probability Measures and the Skorokhod Representation Theorem

V. I. Bogachev, A. V. Kolesnikov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (3179 kB) Citations (12)

DOI: https://doi.org/10.4213/tvp3944

Abstract: We prove that for the wide class of spaces X and Y (including completely regular Souslin spaces), every open surjective mapping $f\colon X\to Y$ induces the open mapping $\hat f\colon\mu\mapsto\mu\circ f^{-1}$ between the spaces of probability measures ${\mathcal P} (X)$ and ${\mathcal P} (Y)$. We discuss the existence of continuous inverse mappings for $\hat f$ and connections with the Skorokhod representation theorem and its generalizations.

Keywords: weak convergence of probability measures, Skorokhod representation, open mapping, continuous selection.

Received: 09.06.1999

English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 1, Pages 20–38
DOI: https://doi.org/10.1137/S0040585X97978701

Bibliographic databases:

Language: Russian

Citation: V. I. Bogachev, A. V. Kolesnikov, “Open Mappings of Probability Measures and the Skorokhod Representation Theorem”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 3–27; Theory Probab. Appl., 46:1 (2002), 20–38

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tvp3944

https://doi.org/10.4213/tvp3944

https://www.mathnet.ru/eng/tvp/v46/i1/p3

This publication is cited in the following 12 articles:

Adam Jakubowski, “Probability on Submetric Spaces”, Annales Mathematicae Silesianae, 37:2 (2023), 138
P. A. Borodin, I. A. Ibragimov, B. S. Kashin, V. V. Kozlov, A. V. Kolesnikov, S. V. Konyagin, E. D. Kosov, O. G. Smolyanov, N. A. Tolmachev, D. V. Treshchev, A. V. Shaposhnikov, S. V. Shaposhnikov, A. N. Shiryaev, A. A. Shkalikov, “Vladimir Igorevich Bogachev (on his 60th birthday)”, Russian Math. Surveys, 76:6 (2021), 1149–1157
Bogachev V.I., Malofeev I.I., “Kantorovich Problems and Conditional Measures Depending on a Parameter”, J. Math. Anal. Appl., 486:10 (2020), 123883
Tateishi H., “The Skorokhod Representation Theorem For Young Measures”, Trans. Am. Math. Soc., 372:9 (2019), 6589–6602
Pratelli L., Rigo P., “On the Existence of Continuous Processes With Given One-Dimensional Distributions”, Electron. Commun. Probab., 24 (2019), 46
Roininen L., Piiroinen P., Lehtinen M., “Constructing Continuous Stationary Covariances as Limits of the Second-Order Stochastic Difference Equations”, Inverse Probl. Imaging, 7:2 (2013), 611–647
Valov V., “Probability measures and Milyutin maps between metric spaces”, J. Math. Anal. Appl., 350:2 (2009), 723–730
V. I. Bogachev, A. V. Kolesnikov, “Integrability of Absolutely Continuous Transformations of Measures and Applications to Optimal Mass Transportation”, Theory Probab. Appl., 50:3 (2006), 367
V. I. Bogachev, A. V. Kolesnikov, “Integrability of absolutely continuous measure transformations and applications to optimal transportation”, Theory Probab. Appl., 50:3 (2006), 367–385
Kolesnikov A.V., “Convexity inequalities and optimal transport of infinite-dimensional measures”, J. Math. Pures Appl. (9), 83:11 (2004), 1373–1404
Banakh T., Chigogidze A., Fedorchuk V., “On spaces of $\sigma$-additive probability measures”, Topology Appl., 133:2 (2003), 139–155
Banakh T.O., Bogachev V.I., Kolesnikov A.V., “Topological spaces with Prokhorov and Skorokhod properties”, Dokl. Math., 64:2 (2001), 244–247

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Theory of Probability and its Applications

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