Maximally truncated resetting diffusion with an absorbing external circular boundary

Abstract

Truncated resetting processes reset a stochastic process a finite number of times to a specific state or set of states. In this paper, we analyze the effects of two maximally truncated resetting protocols, which permit at most one reset, on diffusing particles confined by an absorbing external circular boundary. The first protocol involves deterministic resetting, where the particle is reset to a preset time if it has not been absorbed at the boundary. The second protocol, stochastic resetting, allows at most one reset at a random time, selected from an exponentially decaying resetting-time distribution, provided the particle remains unabsorbed. For both protocols, we derive exact analytical expressions for key metrics: occupation probability, survival probability, first passage time density, mean first passage time, and global mean first passage time.