Unified approach to reset processes and application to coupling between process and reset
arXiv:1903.08055
Abstract
We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the conditions for existence and equality of their stationary values with and without reset. For intermittent reset times, we derive exact asymptotic expressions for observables that vary asymptotically as a power of time. We illustrate the general approach with general and particular results for the power spectral density, and moments of subdiffusive processes. We focus on coupling of the process and reset via a diffusion-decay process with microscopic dependence between transport and decay. In contrast to the uncoupled case, we find that restarting the particle upon decay does not produce a probability current equal to the decay rate, but instead drastically alters the time dependence of the decay rate and the resulting current.
15 pages, 2 figures, corrected copying error in (S42), homogenize terminology, v3 add references, improve title
References in corpus (29)
- Diffusion with Stochastic Resetting
- Intermittent search strategies
- First Passage Under Restart
- First order transition for the optimal search time of Lévy flights with resetting
- Optimal stochastic restart renders fluctuations in first passage times universal
- Diffusion under time-dependent resetting
- Run and tumble particle under resetting: a renewal approach
- Diffusion in a potential landscape with stochastic resetting
- Dynamical transition in the temporal relaxation of stochastic processes under resetting
- Stochastic resetting in backtrack recovery by RNA polymerases
- Diffusion with stochastic resetting at power-law times
- Fluctuating interfaces subject to stochastic resetting
- The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
- Spectral content of a single non-Brownian trajectory
- Stochastic multiplicative processes with reset events
- Large deviations for Markov processes with resetting
- Scaled Brownian motion with renewal resetting
- Quantum dynamics with stochastic reset
- First passage under restart with branching
- Non-renewal resetting of scaled Brownian motion
- Path-integral formalism for stochastic resetting: Exactly solved examples and shortcuts to confinement
- Transport properties and first arrival statistics of random searches with stochastic reset times
- Spectral properties of simple classical and quantum reset processes
- On subdiffusive continuous time random walks with stochastic resetting
- Properties of additive functionals of Brownian motion with resetting
- Long time scaling behaviour for diffusion with resetting and memory
- Phase transitions in large deviations of reset processes
- Diffusion with Resetting Inside a Circle
- Random Search with Memory in Patchy Media: Exploration-Exploitation Tradeoff