Moment conditions for a sequence with negative drift to be uniformly bounded in L^r

Robin Pemantle; Jeffrey S. Rosenthal

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Moment conditions for a sequence with negative drift to be uniformly bounded in L^r

Robin Pemantle·Jeffrey S. Rosenthal

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Abstract

Suppose a sequence of random variables {X_n} has negative drift when above a certain threshold and has increments bounded in L^p. When p>2 this implies that EX_n is bounded above by a constant independent of n and the particular sequence {X_n}. When p=<2 there are counterexamples showing this does not hold. In general, increments bounded in L^p lead to a uniform L^r bound on X_n^+ for any r =p-1. These results are motivated by questions about stability of queueing networks.

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Robin Pemantle, Jeffrey S. Rosenthal. 2004-04-05. Moment conditions for a sequence with negative drift to be uniformly bounded in L^r. https://arxiv.org/abs/math/0404093

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