Subdiffusive search with home returns via stochastic resetting: a subordination scheme approach

Abstract

Stochastic resetting with home returns is widely found in various manifestations in life and nature. Using the solution to the home return problem in terms of the solution to the corresponding problem without home returns (Pal et al 2020 Phys. Rev. Res. 2 043174), we develop a theoretical framework for search with home returns in the case of subdiffusion. This makes a realistic description of restart by accounting for random walks with random stops. The model considers stochastic processes, arising from Brownian motion subordinated by an inverse infinitely divisible process (subordinator).