# On subdiffusive continuous time random walks with stochastic resetting

## TL;DR

This paper investigates two models of subdiffusive processes with stochastic resetting, deriving exact statistical properties and exploring their potential applications in biological data analysis.

## Contribution

It introduces and analyzes two distinct models of subdiffusion with resetting, highlighting their non-Markovian differences and providing exact solutions for key statistical measures.

## Key findings

- Derived exact moments and stationary distributions for both models
- Identified differences due to non-Markovian nature of subdiffusion
- Extended models to include external forces like constant drift

## Abstract

We analyze two models of subdiffusion with stochastic resetting. Each of them consists of two parts: subdiffusion based on the continuous-time random walk (CTRW) 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 times 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.