An occupation time related potential measure for diffusion processes

doi:10.1007/s11464-017-0625-4

Front. Math. China

2017, Vol. 12

Issue (3) : 559-582 https://doi.org/10.1007/s11464-017-0625-4

RESEARCH ARTICLE

An occupation time related potential measure for diffusion processes

Ye CHEN¹(

), Yingqiu LI², Xiaowen ZHOU³

¹. Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone and College of Mathematics and Computational Science, Hunan University of Arts and Science, Changde 415000, China
². School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha 410114, China
³. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada

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Abstract

In this paper, for homogeneous diffusion processes, the approach of Y. Li and X. Zhou [Statist. Probab. Lett., 2014, 94: 48–55] is adopted to find expressions of potential measures that are discounted by their joint occupation times over semi-infinite intervals (−∞, a) and (a,∞). The results are expressed in terms of solutions to the differential equations associated with the diffusions generator. Applying these results, we obtain more explicit expressions for Brownian motion with drift, skew Brownian motion, and Brownian motion with two-valued drift, respectively.

Keywords Laplace transform occupation time potential measure exit time time-homogeneous diffusion Brownian motion with two-valued drift skew Brownian motion

Corresponding Author(s): Ye CHEN

Issue Date: 20 April 2017

Cite this article:

Ye CHEN,Yingqiu LI,Xiaowen ZHOU. An occupation time related potential measure for diffusion processes[J]. Front. Math. China, 2017, 12(3): 559-582.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-017-0625-4
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I3/559

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