What random variable generates a bounded potential?

[摘要] It is known that if a predictable nondecreasing process generatesa bounded potential, then its final value satisfies the Garsiainequality. We prove the converse, that is, a randomvariable satisfying the Garsia inequality generates a boundedpotential. We also propose some useful relations between theGarsia inequality and the Cramer conditions, and different wayshow to construct a potential.

[学科分类] 应用数学