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


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