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

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

2004-04-05

arxiv.org/abs/math/0404093v1

Stoch. Proc. Appl., 82, 143 - 155 (1999)

Mathematics

Probability

18 pages

Scientific paper

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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