Moment conditions for a sequence with negative drift to be uniformly bounded in Lr

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 EXn is bounded above by a constant independent of n and the particular sequence {X-n}. When p less than or equal to 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, but not for r greater than or equal to p -1. These results are motivated by questions about stability of queueing networks. (C) 1999 Elsevier Science B.V. All rights reserved.