Diffusion occupation time before exiting

Abstract

Using the approach of D. Landriault et al. and B. Li and X. Zhou, for a one-dimensional time-homogeneous diffusion process X and constants c<a<b<d, we find expressions of double Laplace transforms of the form , where T_x denotes the first passage time of level x. As applications, we find explicit Laplace transforms of the corresponding occupation time and occupation density for the Brownian motion with two-valued drift and that of occupation time for the skew Ornstein-Uhlenbeck process, respectively. Some known results are also recovered.

Keywords

Diffusion / exit problem / occupation time / occupation density / local time / Brownian motion with two-valued drift / skew Ornstein-Uhlenbeck (OU) process

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg