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

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 impl ies that EXn is bounded above by a constant independent of n and the partic ular sequence {X-n}. When p less than or equal to 2 there are counterexampl es showing this does not hold. In general, increments bounded in L-P lead t o a uniform L-r bound on X-n(+) for any r < p- 1, but not for r greater tha n or equal to p -1. These results are motivated by questions about stabilit y of queueing networks. (C) 1999 Elsevier Science B.V. All rights reserved.