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Advances in Mathematical Physics
Volume 2015, Article ID 627423, 5 pages
http://dx.doi.org/10.1155/2015/627423
Research Article

The Intersection Probability of Brownian Motion and SLEκ

1Department of Statistics and Financial Mathematics, School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
2School of Science, Guangxi University for Nationalities, Nanning, Guangxi 530006, China

Received 29 May 2015; Accepted 4 August 2015

Academic Editor: Andrei D. Mironov

Copyright © 2015 Shizhong Zhou and Shiyi Lan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

By using excursion measure Poisson kernel method, we obtain a second-order differential equation of the intersection probability of Brownian motion and . Moreover, we find a transformation such that the second-order differential equation transforms into a hypergeometric differential equation. Then, by solving the hypergeometric differential equation, we obtain the explicit formula of the intersection probability for the trace of the chordal and planar Brownian motion started from distinct points in an upper half-plane .