A “coboundary” theorem for sums of random variables taking their values in a Banach space

Richard C. Bradley

Vol. 178 (1997), No. 2, 201–224

DOI: 10.2140/pjm.1997.178.201

Abstract

Klaus Schmidt proved that if a strictly stationary sequence of (say) real-valued random variables is such that the family of distributions of its partial sums is tight, then that sequence is a “coboundary”. Here Schmidt’s result is extended to some (not necessarily stationary) sequences of random variables taking their values in a separable real Banach space.

Milestones

Received: 2 August 1995

Published: 1 April 1997