ON THE MOMENTS OF LADDER EPOCHS FOR DRIFTLESS RANDOM-WALKS

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/28057

Title:	ON THE MOMENTS OF LADDER EPOCHS FOR DRIFTLESS RANDOM-WALKS
Authors:	CHOW,YS
Contributors:	數學研究所
Date:	1994
Issue Date:	2010-06-29 19:41:02 (UTC+8)
Publisher:	中央大學
Abstract:	Let X, X1, X2, ... be i.i.d. S(n) = SIGMA1(n)X(j), E\X\ > 0, E(X) = 0 and tau = inf{n greater-than-or-equal-to 1 : S(n) greater-than-or-equal-to 0}. By Wald's equation, E(tau) = infinity. If E(X2) < infinity, then by a theorem of Burkholder and Gundy (1970), E(tau1/2) = infinity. In this paper, we prove that if E((X-)2) < infinity, then E(tau1/2) = infinity. When X is integer-valued and X greater-than-or-equal-to -1 a.s., a necessary and sufficient condition for E(tau1-1/p) < infinity, p > 1, is SIGMAn-1-1/P E\S(n)\ < infinity.
Relation:	JOURNAL OF APPLIED PROBABILITY
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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