Moment conditions for a sequence with negative drift to be uniformly bounded in Lr
Abstract
Suppose a sequence of random variables Xn has negative drift when above a certain threshold and has increments bounded in Lp. When p>2 this implies that EXn is bounded above by a constant independent of n and the particular sequence Xn. When p=<2 there are counterexamples showing this does not hold. In general, increments bounded in Lp lead to a uniform Lr bound on Xn+ for any r<p-1, but not for r>=p-1. These results are motivated by questions about stability of queueing networks.
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