Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 250-257
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A. V. Sudakov. A counterexample to the conjecture on monotonicity of an integral with respect to Gaussian measure. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 3, Tome 260 (1999), pp. 250-257. http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a16/
@article{ZNSL_1999_260_a16,
author = {A. V. Sudakov},
title = {A counterexample to the conjecture on monotonicity of an integral with respect to {Gaussian} measure},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {250--257},
year = {1999},
volume = {260},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a16/}
}
TY - JOUR
AU - A. V. Sudakov
TI - A counterexample to the conjecture on monotonicity of an integral with respect to Gaussian measure
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1999
SP - 250
EP - 257
VL - 260
UR - http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a16/
LA - ru
ID - ZNSL_1999_260_a16
ER -
%0 Journal Article
%A A. V. Sudakov
%T A counterexample to the conjecture on monotonicity of an integral with respect to Gaussian measure
%J Zapiski Nauchnykh Seminarov POMI
%D 1999
%P 250-257
%V 260
%U http://geodesic.mathdoc.fr/item/ZNSL_1999_260_a16/
%G ru
%F ZNSL_1999_260_a16
It is shown that for the Kantorovich metrics $\varkappa$ on probability measures for centered Gaussian measures $\gamma$ defined on Euclidean space $E$ of random variables $X$ the integral $$ I(\gamma)=\iint\limits_{E\oplus E}\varkappa(\mathscr L(X_1),\mathscr L(X_2))(\gamma\otimes\gamma)\,d(X_1,X_2), $$ is not always monotonic in $\gamma$.
