Homing Problems for Diffusion Processes with Random Resettings

Abstract

The problem of minimizing the expected time spent by one-dimensional stochastic processes in a given interval is considered in the case of diffusion processes with random resettings. At random times that occur according to a Poisson process, the controlled diffusion process jumps from its current position to a fixed value. The differential equation satisfied by the value function is given and particular problems are solved explicitly.