Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 1, Pages 97-106
What random variable generates a bounded potential?
Department of Mathematics, Kiev National University, 64 Vladimirskaya Street, Kiev 01033, Ukraine
Received 29 March 2002; Revised 4 October 2003
Copyright © 2004 N. Kartashov and Yu. Mishura. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is known that if a predictable nondecreasing process generates
a bounded potential, then its final value satisfies the Garsia
inequality. We prove the converse, that is, a random
variable satisfying the Garsia inequality generates a bounded
potential. We also propose some useful relations between the
Garsia inequality and the Cramer conditions, and different ways
how to construct a potential.