Hostname: page-component-7479d7b7d-rvbq7 Total loading time: 0 Render date: 2024-07-10T22:45:04.843Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Friedman, A. (1975). Stochastic Differential Equations and Applications, Vol. I. Academic Press, New York.Google Scholar
Menshikov, M., and Williams, R. J. (1996). Passage-time moments for continuous nonnegative stochastic processes and applications. Adv. Appl. Prob. 28, 747–762.Google Scholar
Varadhan, S. R. S., and Williams, R. J. (1985). Brownian motion in a wedge with oblique reflection. Commun. Pure Appl. Math. 38, 405–443.CrossRefGoogle Scholar
Williams, R. J. (1985). Recurrence classification and invariant measure for reflecting Brownian motion in a wedge. Ann. Prob. 13, 758–778.Google Scholar