Scaled Brownian motion with renewal resetting

Abstract

We investigate an intermittent stochastic process in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha -1}$ with $\alpha >0$ (scaled Brownian motion) is stochastically reset to its initial position, and starts anew. \color{black} In the present work we discuss the situation, in which the memory on the value of the diffusion coefficient at a resetting time is erased, so that the whole process is a fully renewal one. The situation when the resetting of coordinate does not affect the diffusion coefficient's time dependence is considered in the other work of this series. We show that the properties of the probability densities in such processes (erazing or retaining the memory on the diffusion coefficient) are vastly different. \color{black} In addition we discuss the first passage properties of the scaled Brownian motion with renewal resetting and consider the dependence of the efficiency of search on the parameters of the process.

References in corpus (25)

• Diffusion with Stochastic Resetting
• Intermittent search strategies
• Diffusion with Optimal Resetting
• 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
• Diffusion with resetting in arbitrary spatial dimension
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• 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
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• The Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem
• Optimal first arrival times in Lévy flights with resetting
• Optimal diffusive search: nonequilibrium resetting versus equilibrium dynamics
• Boosting search by rare events
• Stochastic Search with Poisson and Deterministic Resetting
• Effects of refractory period on stochastic resetting
• Scaled Brownian motion as a mean field model for continuous time random walks
• Single-molecule theory of enzymatic inhibition predicts the emergence of inhibitor-activator duality
• Non-renewal resetting of scaled Brownian motion
• Transport properties and first arrival statistics of random searches with stochastic reset times
• Mean first passage time of active Brownian particle in one dimension
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics

Cited by in corpus (55)

• Stochastic Resetting and Applications
• Experimental realization of diffusion with stochastic resetting
• Stochastic resetting: A (very) brief review
• Resetting processes with non-instanteneous return
• Symmetric Exclusion Process under Stochastic Resetting
• Non-renewal resetting of scaled Brownian motion
• Diffusion with stochastic resetting is invariant to return speed
• Transport properties of random walks under stochastic non-instantaneous resetting
• First passage under restart for discrete space and time: application to one dimensional confined lattice random walks
• Geometric Brownian Motion under Stochastic Resetting: A Stationary yet Non-ergodic Process
• Invariants of motion with stochastic resetting and space-time coupled returns
• Properties of additive functionals of Brownian motion with resetting
• Restart expedites quantum walk hitting times
• Extremal statistics for stochastic resetting systems
• Stochastic resetting by a random amplitude
• Subdiffusion equation with Caputo fractional derivative with respect to another function
• Random acceleration process under stochastic resetting
• Stochastic resetting on comb-like structures
• Continuous time random walks under power-law resetting
• Diffusion with Partial Resetting
• Diffusion processes with Gamma-distributed resetting and non-instantaneous returns
• Diffusion with Local Resetting and Exclusion
• Resetting transition is governed by an interplay between thermal and potential energy
• Continuous time random walks and Lévy walks with stochastic resetting
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Brownian motion under non-instantaneous resetting in higher dimensions
• Robust random search with scale-free stochastic resetting
• A Unified Approach to Gated Reactions on Networks
• General approach to stochastic resetting
• Generating Entanglement by Quantum Resetting
• Superstatistical approach of the anomalous exponent for scaled Brownian motion
• Random walks with stochastic resetting in complex networks: a discrete time approach
• Zero-current Nonequilibrium State in Symmetric Exclusion Process with Dichotomous Stochastic Resetting
• Kuramoto model subject to subsystem resetting: How resetting a part of the system may synchronize the whole of it
• Non-linear diffusion with stochastic resetting
• Mean-performance of Sharp Restart II: Inequality Roadmap
• Tail-behavior roadmap for sharp restart
• Measurement-induced resetting in open quantum systems
• Random acceleration process on finite intervals under stochastic restarting
• Stochastic resetting with refractory periods: pathway formulation and exact results
• Dichotomous flow with thermal diffusion and stochastic resetting
• Manipulating phases in many-body interacting systems with subsystem resetting
• Stochastic resetting in a nonequilibrium environment
• Continuous Gated First-Passage Processes
• Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting
• Anomalous diffusion of scaled Brownian tracers
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Unified approach to reset processes and application to coupling between process and reset
• Conditioned backward and forward times of diffusion with stochastic resetting: a renewal theory approach
• Local resetting with geometric confinement
• Search of stochastically gated targets with diffusive particles under resetting
• First-Passage-Driven Boundary Recession
• Designing non-equilibrium states of quantum matter through stochastic resetting
• Optimal detection of quantum states via projective measurements
• Thermodynamics of quantum-jump trajectories of open quantum systems subject to stochastic resetting