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Theory Stoch. Process., 2016, Volume 21(37), Issue 1, Pages 1–11 (Mi thsp115)  

On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes

V. I. Bogachevabc, A. F. Miftakhovabc

a Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b St.-Tikhon’s Orthodox Humanitarian University, Moscow, Russia
c National Research University Higher School of Economics, Moscow, Russia

Abstract: We study conditions on metrics on spaces of measurable functions under which weak convergence of Borel probability measures on these spaces follows from weak convergence of finite-dimensional projections of the considered measures.

Keywords: Convergence in measure, weak convergence, finite-dimensional distributions.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-90406
14-01-00237
Universität Bielefeld SFB 701
Our work has been supported by the RFBR grants 14-01-90406, 14-01-00237 and the SFB 701 at Bielefeld University.


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Bibliographic databases:

Document Type: Article
MSC: 46G12, 60B10, 60G07
Language: English

Citation: V. I. Bogachev, A. F. Miftakhov, “On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes”, Theory Stoch. Process., 21(37):1 (2016), 1–11

Citation in format AMSBIB
\Bibitem{BogMif16}
\by V.~I.~Bogachev, A.~F.~Miftakhov
\paper On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes
\jour Theory Stoch. Process.
\yr 2016
\vol 21(37)
\issue 1
\pages 1--11
\mathnet{http://mi.mathnet.ru/thsp115}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3571407}


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