Subdiffusive search with home returns via stochastic resetting: a subordination scheme approach. (English) Zbl 1505.60050
Summary: 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 [A. Pal, Ł. Kuśmierz and S. Reuveni, “Search with home returns provides advantage under high uncertainty”, Phys. Rev. Res. 2, No. 4, Article ID 043174, 15 p. (2020; doi:10.1103/PhysRevResearch.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).
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