Journal of Applied Mathematics and Stochastic Analysis 
Volume 2004 (2004), Issue 1, Pages 97-106
doi:10.1155/S104895330420301X

What random variable generates a bounded potential?

N. Kartashov and Yu. Mishura

 Department of Mathematics, Kiev National University, 64 Vladimirskaya Street, Kiev 01033, Ukraine
Received 29 March 2002; Revised 4 October 2003

Abstract

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.