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

Robin Pemantle and Jeffrey S. Rosenthal

Stochastic Processes and their Applications, 1999, vol. 82, issue 1, 143-155

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 0sequence {Xn}. When p[less-than-or-equals, slant]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

Keywords: Lp; pth; moments; Supermartingale; Martingale; Linear; boundary; Lyapunov; function; Stochastic; adversary; Queueing; networks (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (3)

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