N. Kartashov, Yu. Mishura, "What random variable generates a bounded potential?", International Journal of Stochastic Analysis, vol. 2004, Article ID 864541, 10 pages, 2004. https://doi.org/10.1155/S104895330420301X
What random variable generates a bounded potential?
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.
Copyright © 2004 Hindawi Publishing Corporation. 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.