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Passage-time moments for continuous non-negative stochastic processes and applications

Part of:Markov processesStochastic processes

Published online by Cambridge University Press:  01 July 2016

M. Menshikov and
R. J. Williams
M. Menshikov*
Affiliation:
Moscow State University
R. J. Williams*
Affiliation:
University of California at San Diego
*
∗ Postal address: Laboratory of Large Random Systems, Moscow State University, Moscow 119899, Russia. Research supported in part by a grant from the International Science Foundation (SOROS).
∗∗ Postal address: Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0112, USA. Research supported in part by NSF Grant GER 9023335.
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Abstract

We give criteria for the finiteness or infiniteness of the passage-time moments for continuous non-negative stochastic processes in terms of sub/supermartingale inequalities for powers of these processes. We apply these results to one-dimensional diffusions and also reflected Brownian motion in a wedge. The discrete-time analogue of this problem was studied previously by Lamperti and more recently by Aspandiiarov, Iasnogorodski and Menshikov [2]. Our results are continuous analogues of those in [2], but our proofs are direct and do not rely on approximation by discrete-time processes.

Keywords

PASSAGE-TIME MOMENTSSUB/SUPERMARTINGALE INEQUALITIESDIFFUSIONSREFLECTED BROWNIAN MOTION IN A WEDGE

MSC classification

Primary:60G44: Martingales with continuous parameter60J60: Diffusion processes

Information

Type
General Applied Probablity
Information
Advances in Applied Probability , Volume 28 , Issue 3 , September 1996, pp. 747 - 762
Copyright
Copyright © Applied Probability Trust 1996 

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