Table of Contents
ISRN Applied Mathematics
Volume 2013 (2013), Article ID 865347, 5 pages
http://dx.doi.org/10.1155/2013/865347
Research Article

On the Distribution of First Exit Time for Brownian Motion with Double Linear Time-Dependent Barriers

School of Mathematics and Computer Science, Anhui Normal University, Wuhu 241000, China

Received 2 July 2013; Accepted 28 August 2013

Academic Editors: G. Kyriacou and C. Lu

Copyright © 2013 Lin Xu and Dongjin Zhu. 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

This paper focuses on the first exit time for a Brownian motion with a double linear time-dependent barrier specified by , , (, , ). We are concerned in this paper with the distribution of the Brownian motion hitting the upper barrier before hitting the lower linear barrier. The main method we applied here is the Girsanov transform formula. As a result, we expressed the density of such exit time in terms of a finite series. This result principally provides us an analytical expression for the distribution of the aforementioned exit time and an easy way to compute the distribution of first exit time numerically.