Frontiers of Mathematics in China >
An occupation time related potential measure for diffusion processes
Received date: 21 Oct 2015
Accepted date: 26 Dec 2016
Published date: 20 Apr 2017
Copyright
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.
Ye CHEN , Yingqiu LI , Xiaowen ZHOU . An occupation time related potential measure for diffusion processes[J]. Frontiers of Mathematics in China, 2017 , 12(3) : 559 -582 . DOI: 10.1007/s11464-017-0625-4
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