To reset, or not to reset, that is the question

The first passage statistics of stochastic processes play an important role in understanding the behavior of some useful models in physical chemistry, biology, finance, computer science and other fields. Allowing the underlying stochastic process to restart or reset to its initial condition at certain intervals can dramatically change these first passage statistics. In this discussion, we will review some results for continuous-time stochastic processes, and then examine some of the effects of resetting on discrete-time processes, paying special attention to two important reset time distributions: geometric and sharp (deterministic). In particular, we will consider the circumstances under which resetting can increase or reduce the mean hitting time of a process