IJPAM: Volume 22, No. 4 (2005)
CONDITIONS FOR ALMOST SURE CONVERGENCE
George Stoica
Department of Mathematical Sciences
University of New Brunswick Saint John
P.O. Box 5050, Saint John NB, E2L 4L5, CANADA
e-mail: stoica@unbsj.ca
Department of Mathematical Sciences
University of New Brunswick Saint John
P.O. Box 5050, Saint John NB, E2L 4L5, CANADA
e-mail: stoica@unbsj.ca
Abstract.We study the almost sure convergence of normalized random vectors when
the limit of the cumulant generating functions does not exist or one is unable to find
it. As such, familiar tools like differentiability, convexity, exponential tightness, etc. are no longer at hand. We give examples and applications in both finite and
infinite dimension.
Received: May 10, 2005
AMS Subject Classification: 60B12
Key Words and Phrases: almost sure convergence, cumulant generating function, convex dominating function, exponential submartingale condition
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 22
Issue: 4
