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The Joint Laplace Transforms for Diffusion Occupation Times

Part of: Markov processes Stochastic processes

Published online by Cambridge University Press:  04 January 2016

Bin Li  and
Xiaowen Zhou
Bin Li*
Affiliation:
University of Iowa
Xiaowen Zhou*
Affiliation:
Concordia University
*
∗ Current address: Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada. Email address: bin.li@uwaterloo.ca
∗∗ Postal address: Department of Mathematics and Statistics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada. Email address: xiaowen.zhou@concordia.ca
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Abstract

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In this paper we adopt the perturbation approach of Landriault, Renaud and Zhou (2011) to find expressions for the joint Laplace transforms of occupation times for time-homogeneous diffusion processes. The expressions are in terms of solutions to the associated differential equations. These Laplace transforms are applied to study ruin-related problems for several classes of diffusion risk processes.

Keywords

Exit problemoccupation timeruin probabilitytime-homogeneous diffusion

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60G17: Sample path properties
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 4 , December 2013 , pp. 1049 - 1067
Copyright
© Applied Probability Trust 

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