The Mean Escape Time for a Narrow Escape Problem with Multiple Switching Gates

Abstract

This article deals with the narrow escape problem when there are two gates which open alternatively in a random way. We set up the problem and carry out a rigorous asymptotic analysis to derive the mean escape time (MET) for a Brownian particle inside a domain to exit the domain through the switching gates. We show that the MET decreases as the switching rate between the gates increases, and we give upper and lower bounds for the decay rate. We then consider the case when there are multiple switching gates and derive the leading-order term of the asymptotic expansion of the MET.