Continuous time random walks under Markovian resetting

Méndez, Vicenç; Masó-Puigdellosas, Axel; Sandev, Trifce; Campos, Daniel

doi:10.1103/physreve.103.022103

Cited by 26 publications

(14 citation statements)

References 35 publications

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“…The existence of the invariant distribution for the process X and its shape depends on signs of the parameters γ 0 , γ 1 , which determine the boundary conditions to equation (21).…”

Section: Invariant Measuresmentioning

confidence: 99%

“…First, we are interested in first passage probabilities of the Kac-Ornstein-Uhlenbeck process, Sections and . This subject is related to applications of persistent random walks which are still of interest, [17,20,21,27,33]. Second, we study invariant measures for Markov process which is formed by the Kac-Ornstein-Uhlenbeck process X and the underlying state process ε, X (t), ε(t) , Sections and .…”

Section: Introductionmentioning

confidence: 99%

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First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes

Ratanov¹

2021

Preprint

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In this paper, we study Ornstein-Uhlenbeck processes with Markov modulation, whose parameters depend on an external underlying two-state Markov process ε. Conditional mean and variance of such processes under given modulation are investigated from the point of view of the first passage probabilities and invariant measures. It is also studied the limiting behaviour under scaling conditions similar to Kac's scaling.

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“…The existence of the invariant distribution for the process X and its shape depends on signs of the parameters γ 0 , γ 1 , which determine the boundary conditions to equation (21).…”

Section: Invariant Measuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes

Ratanov¹

2021

Preprint

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“…Depending on the type of random walk and the characteristics of the resetting mechanism, the overall process may reach an equilibrium state [2] and have an optimal strategy to reach a fixed target [3]. The mean first passage time (MFPT) of a random walker to reach a target located at a given position has been often used to determine the efficiency of resetting for different types of motion [4] and reset time distributions [5][6][7]. In general, the presence of a safe and fresh reset renders the walker a new opportunity to reach the target whenever it gets far from it.…”

Section: Introductionmentioning

confidence: 99%

“…In the particular case where the resetting is Markovian (i.e. it restarts at a constant rate), this process has been shown to exhibit an optimal point for many types of random walk as in the case of a diffusive walker [8], subdiffusive [9,10], performing Lévy flights [11,12] or under a combination of long-distance jumps interrupted by rests of large duration [4]. Random walks under resetting in a bounded domain have also attracted some attention.…”

Section: Introductionmentioning

confidence: 99%

Non-standard diffusion under Markovian resetting in bounded domains

Méndez,

Masó-Puigdellosas,

Campos

2022

Preprint

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We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time distribution between consecutive short jumps. We investigate the existence of an optimal reset rate, which minimizes the mean exit passage time, in terms of the statistical properties of the waiting time probability. Generalizing previous results restricted to Markovian random walks, we here find that, depending on the value of the relative standard deviation of the waiting time probability, resetting can be either (i) never beneficial, (ii) beneficial depending on the distance of the reset to the boundary, or (iii) always beneficial.

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“…Two key features of diffusion processes with resetting are that (i) the system always achieves a nontrivial nonequilibrium steady state, and (ii) in the presence of a target, there exists an optimal rate for which the search time is finite and minimum [37,38]. No wonder the occurrence of such intriguing characteristics triggers exploring its different variants, namely, resetting with several processes such as continuous-time random walks [39], fractional Brownian motions [40], Lévy flights [41], underdamped diffusion [42], velocity-jump processes [43] and others [44,45]. Furthermore, the effect of various confining potentials [46][47][48] and diffusivities [49] on the resetting mechanism has been investigated thoroughly over the past few years.…”

Section: Introductionmentioning

confidence: 99%

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise

Goswami,

Chakrabarti

2021

Preprint

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We study the dynamics of an overdamped Brownian particle subjected to Poissonian stochastic resetting in a nonthermal bath, characterized by a Poisson white noise and a Gaussian noise. Applying the renewal theory we find an exact analytical expression for the spatial distribution at the steady state. Unlike the single exponential distribution as observed in the case of a purely thermal bath, the distribution is double exponential. Relaxation of the transient spatial distributions to the stationary one, for the limiting cases of Poissonian rate, is investigated carefully. In addition, we study the first-arrival properties of the system in the presence of a delta-function sink with strength κ, where κ = 0 and κ = ∞ correspond to fully nonreactive and fully reactive sinks, respectively. We explore the effect of two competitive mechanisms: the diffusive spread in the presence of two noises and the increase in probability density around the initial position due to stochastic resetting. We show that there exists an optimal resetting rate, which minimizes the mean first-arrival time (MFAT) to the sink for a given value of the sink strength. We also explore the effect of the strength of the Poissonian noise on MFAT, in addition to sink strength. Our formalism generalizes the diffusion-limited reaction under resetting in a nonequilibrium bath and provides an efficient search strategy for a reactant to find a target site, relevant in a range of biophysical processes

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Continuous time random walks under Markovian resetting

Cited by 26 publications

References 35 publications

First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes

First-passage probabilities and invariant distributions of Kac-Ornstein-Uhlenbeck processes

Non-standard diffusion under Markovian resetting in bounded domains

Stochastic resetting and first arrival subjected to Gaussian noise and Poisson white noise

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