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Passage time moments for multidimensional diffusions

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

S. Balaji  and
S. Ramasubramanian
S. Balaji*
Affiliation:
Indian Statistical Institute, Bangalore
S. Ramasubramanian*
Affiliation:
Indian Statistical Institute, Bangalore
*
∗Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore 560 059, India.
∗Postal address: Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, Bangalore 560 059, India.
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Abstract

Let τr denote the hitting time of B(0:r) for a multidimensional diffusion process. We give verifiable criteria for finiteness/infiniteness of As an application we exhibit classes of diffusion processes which are recurrent but is infinite for all p > 0, |x| > r > 0; this includes the two-dimensional Brownian motion and the reflecting Brownian motion in a wedge with a certain parameter α = 0.

Keywords

Hitting timerecurrent diffusionsgeneratordiffusion coefficientssub/super-martingalesreflecting Brownian motion in a wedge

MSC classification

Primary: 60J60: Diffusion processes 60J65: Brownian motion
Type
Short Communications
Information
Journal of Applied Probability , Volume 37 , Issue 1 , March 2000 , pp. 246 - 251
Copyright
Copyright © 2000 by The Applied Probability Trust 

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References

Friedman, A. (1975). Stochastic Differential Equations and Applications, Vol. I. Academic Press, New York.Google Scholar
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Williams, R. J. (1985). Recurrence classification and invariant measure for reflecting Brownian motion in a wedge. Ann. Prob. 13, 758–778.Google Scholar