2018/12/31 by Łukasz Kuśmierz, Ewa Gudowska–Nowak, Ewa Gudowska-Nowak · 75 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Computer science #Constant (computer programming) #Continuous-time random walk #Diffusion and Search Dynamics #First-hitting-time model #Hitting time #Markov process #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Physics #Poisson distribution #Poisson point process #Position (finance) #Propagator #Random walk #Reset (finance) #Statistical physics #Statistics #Stochastic process #cond-mat.stat-mech #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.99.052116
published in Physical review. E 99(5), 052116 (American Physical Society) · 11 pages, 5 figures
arxiv created 2019/05/01 · openalex publication_date 2019/05/14 · arxiv updated 2019/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk scheme and independent resetting events generated uniformly in time according to the Poisson point process. In the first model the whole process is reset to the initial state, whereas in the second model only the position is subject to resets. The distinction between these two models arises from the non-Markovian character of the subdiffusive process. We derive exact expressions for the two lowest moments of the full propagator, stationary distributions, and first hitting time statistics. We also show, with an example of a constant drift, how these models can be generalized to include external forces. Possible applications to data analysis and modeling of biological systems are also discussed.