The mean exiting time for the biased correlated random walk characterized by a system of first-order PDEs

Abstract

A biased correlated random walk (BCRW) is a stochastic process that models individual movement and other similar practical phenomena. This paper studies the mean exiting time of a BCRW in a finite interval, subject to a system of first-order PDEs. The interval has two scenarios: (i) both ends are absorbing; and (ii) one end is absorbing and the other end is reflecting. We obtain an exact formula for the mean exiting time of a particle as a function of its speed, turning rates, and initial position. Using the mean exiting time, we also derive the mean first passage time for a particle to reach the boundary. Our approach enables us to infer relevant parameters from experimental data, or to manipulate the mean exiting time and the first passage time by choosing the initial position of the particle suitably. The unbiased case is a special case of the biased case when the right-turning rate equals the left-turning rate.

Keywords:

• Random process
• correlated random walk
• mean exiting time
• mean first passage time

2020 Mathematics Subject Classifications:

• 35F16
• 35F35
• 35F46

Acknowledgments

During his visit from December 2016 to December 2017, the first author, Jianliang Tang, would like to express his gratitude for the hospitality extended to him by the Department of Mathematics at Southern Illinois University Carbondale. This joint work was initiated during his visit

Disclosure statement

No potential conflict of interest was reported by the author(s).