animals foraging for food in the wilderness or a person searching for car keys, often include random resets in time, taking the form of returns to past locations where food was successfully located or the last place a person remembers seeing their keys [@benichou2011]. Recently, there has been a renewed interest in these processes, due to the fact that they can improve the efficiency of certain random search processes and algorithms in terms of mean hitting or first-passage time [@evans2011; @evans2011b; @evans2013; @evans2014; @reuveni2016; @pal2017]. Reset processes have also been studied from a more physical point of view, as they provide a simple model of nonequilibrium processes breaking detailed balance [@manrubia1999; @gupta2014; @roldan2016; @eule2016], as well as of processes showing dynamical phase transitions in their relaxation dynamics [@majumdar2015b], mean first-passage time [@kusmierz2014], or large deviations [@meylahn2015b; @Harris2017; @hollander2018].

These studies follow many previous works in mathematics, in queuing theory and in population dynamics, in particular, on stochastic processes involving some form of random resets, variously referred to as failures, catastrophes, disasters or decimations; see, e.g., [@brockwell1982; @luby1993; @pakes1997; @kumar2000; @cairns2004; @janson2012; @avrachenkov2013; @dharmaraja2015; @montero2017]. Most of these works, as well as those from physics mentioned above, make use of the 