On subdiffusive continuous time random walks with stochastic resetting

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.

arXiv comment11 pages, 5 figures

References in corpus (45)

• Brownian motors: noisy transport far from equilibrium
• Artificial Brownian motors: Controlling transport on the nanoscale
• Fractional calculus and continuous-time finance
• Diffusion with Stochastic Resetting
• Lévy walks
• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Cooperative Cargo Transport by Several Molecular Motors
• First Passage Under Restart
• Ergodic Properties of Fractional Brownian-Langevin Motion
• First order transition for the optimal search time of Lévy flights with resetting
• Anomalous diffusion of phospholipids and cholesterols in a lipid bilayer and its origins
• Stochastic Ergodicity Breaking: a Random Walk Approach
• Optimal stochastic restart renders fluctuations in first passage times universal
• Diffusion under time-dependent resetting
• Diffusion in a potential landscape with stochastic resetting
• Diffusion with resetting in arbitrary spatial dimension
• Probing microscopic origins of confined subdiffusion by first-passage observables
• The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times
• Dynamical transition in the temporal relaxation of stochastic processes under resetting
• Random walks with preferential relocations to places visited in the past and their application to biology
• Non-equilibrium steady states of stochastic processes with intermittent resetting
• Fluctuating interfaces subject to stochastic 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
• First passage and arrival time densities for Lévy flights and the failure of the method of images
• Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces
• Stochastic Search with Poisson and Deterministic Resetting
• Monotonous continuous-time random walks with drift and stochastic reset events
• Restart could optimize the probability of success in a Bernoulli trial
• Effects of refractory period on stochastic resetting
• Péclet number governs transition to acceleratory restart in drift-diffusion
• Localization transition induced by learning in random searches
• Phase transitions in optimal search times: how random walkers should combine resetting and flight scales
• Transition to superdiffusive behavior in intracellular actin-based transport mediated by molecular motors
• Transport properties and first arrival statistics of random searches with stochastic reset times
• A Test for Determining a Subdiffusive Model in Ergodic Systems from Single Trajectories
• Continuous-time random walks with reset events: Historical background and new perspectives
• Molecular motors transporting cargos in viscoelastic cytosol: how to beat subdiffusion with a power stroke?
• Stochastic processes subject to a reset-and-residence mechanism: transport properties and first arrival statistics
• Mesoscopic description of reactions under anomalous diffusion: A case study
• Sub-diffusion in External Potential: Anomalous hiding behind Normal
• Anomalous transport of subdiffusing cargos by single kinesin motors: the role of mechanochemical coupling and anharmonicity of tether
• Anomalous diffusion and generalized Sparre-Andersen scaling
• Optimal potentials for diffusive search strategies

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• Invariants of motion with stochastic resetting and space-time coupled returns
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• Local time of diffusion with stochastic resetting
• Random acceleration process under stochastic resetting
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• Continuous time random walks under power-law resetting
• Diffusive transport on networks with stochastic resetting to multiple nodes
• The cost of stochastic resetting
• Diffusion with Partial Resetting
• Continuous time random walks under Markovian resetting
• Mean-performance of sharp restart I: Statistical roadmap
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• Transient anomalous diffusion in heterogeneous media with stochastic resetting
• Continuous time random walks and Lévy walks with stochastic resetting
• Condensation transition in large deviations of self-similar Gaussian processes with stochastic resetting
• Ornstein-Uhlenbeck process and generalizations: particle's dynamics under comb constraints and stochastic resetting
• Reducing mean first passage times with intermittent confining potentials: a realization of resetting processes
• Anomalous diffusion in random-walks with memory-induced relocations
• Robust random search with scale-free stochastic resetting
• General approach to stochastic resetting
• Instability in the quantum restart problem
• Median and Mode in First Passage under Restart
• Striking universalities in stochastic resetting processes
• Non-linear diffusion with stochastic resetting
• Discrete-time random walks and Lévy flights on arbitrary networks: when resetting becomes advantageous?
• Tail-behavior roadmap for sharp restart
• Effects of mortality on stochastic search processes with resetting
• Measurement-induced resetting in open quantum systems
• Random resetting in search problems
• Non-homogeneous random walks with stochastic resetting: an application to the Gillis model
• Crossover from Anomalous to Normal Diffusion: Ising Model with Stochastic Resetting
• Mean first-encounter times of simultaneous random walkers with resetting on networks
• Unified approach to reset processes and application to coupling between process and reset
• Autocorrelation functions and ergodicity in diffusion with stochastic resetting
• Conditioned backward and forward times of diffusion with stochastic resetting: a renewal theory approach
• Gaussian Process and Levy Walk under Stochastic Non-instantaneous Resetting and Stochastic Rest
• Abrupt transitions in the optimization of diffusion with distributed resetting
• Search of stochastically gated targets with diffusive particles under resetting
• Non-standard diffusion under Markovian resetting in bounded domains
• Poissonian resetting of subdiffusion in a linear potential