Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 4: 843 - 861

DOI: https://doi.org/10.1007/s11464-014-0402-6

RESEARCH ARTICLE

Diffusion occupation time before exiting

  • Yingqiu LI 1 ,
  • Suxin WANG 2 ,
  • Xiaowen ZHOU 3 ,
  • Na ZHU , 1
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  • 1. College of Mathematics and Computing Sciences, Changsha University of Science and Technology, Changsha 410004, China
  • 2. College of Mathematics, Nankai University, Tianjin 300071, China
  • 3. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada

Received date: 19 Feb 2014

Accepted date: 17 Jun 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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 Ex[e-θTd-λ∫0Td1a<Xs<bds;Td<Tc], where Tx 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.

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

Cite this article

Yingqiu LI , Suxin WANG , Xiaowen ZHOU , Na ZHU . Diffusion occupation time before exiting[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 843 -861 . DOI: 10.1007/s11464-014-0402-6

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