V. I. Bogachev, A. F. Miftakhov, “On weak convergence of finite-dimensional and infinite-dimensional distributions of random processes”, Theory Stoch. Process., 2016, Volume 21(37), Issue 1,Pages <nobr>1

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

V. I. Bogachev^abc, A. F. Miftakhov^abc

^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.

MSC: 46G12, 60B10, 60G07

Language: English