Anomalous Transport of Heterogeneous Population and Time-Changed Pólya Process

Sergei Fedotov (), Alexey O. Ivanov and Hong Zhang
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Sergei Fedotov: Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK
Alexey O. Ivanov: Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
Hong Zhang: School of Mathematical Sciences, Chengdu University of Technology, Chengdu 610059, China

Mathematics, 2025, vol. 13, issue 12, 1-12

Abstract: We propose a continuous-time unidirectional random walk model for a heterogeneous population of particles involving subdiffusive trapping effects. In this model, after escaping from the trap, each particle either jumps forward with a random probability or remains in the same place. The population heterogeneity is captured by modeling the jump probability as a beta-distributed random variable. The randomness in this transition parameter generates an effective jump probability with the ensemble self-reinforcement. We derive the limiting probability for the ensemble average of the particle position using an integral subordination formula. We show that the average particle position can be represented by a time-changed Pólya process involving an inverse stable subordinator.

Keywords: heterogeneous population; anomalous transport; ensemble self-reinforcement; time-changed Pólya process; integral subordination formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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