Diffusion with partial resetting

Tal-Friedman, Ofir; Roichman, Yael; Reuveni, Shlomi

doi:10.1103/physreve.106.054116

Cited by 17 publications

(24 citation statements)

References 65 publications

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“…Equation ( 9) is the first main result of the paper, generalising previous results [79][80][81]. In [79] the authors considered the case of deterministic ballistic motion with constant speed and PSR.…”

Section: Propagator For Partial Resettingmentioning

confidence: 54%

“…Going significantly beyond recent work [80,81] reporting the FPE and the stationary PDF for Brownian PSR [80] and the time-dependent PDF in Fourier-Laplace space when the initial condition is at the origin, we here develop a general technique to determine the time-dependent PDF for homogeneous Markov processes with Poissonian resetting, in which the process is partially reset by multiplication with the constant factor 0 < c < 1 at random times T 1 , T 1 + T 2 , . .…”

Section: Introductionmentioning

confidence: 93%

“…The propagator for this process which was not reported in [79] can be found from result (9) by setting p 0 (x, t) = δ(x − vt), where v is the speed. Moreover, the results in [80,81] follow from (9) by setting x 0 = 0 and p 0 (x, t) = (4π Dt) −1/2 exp(−x 2 /(4Dt)).…”

Section: Propagator For Partial Resettingmentioning

confidence: 99%

“…where the space-fractional operator is defined in terms of its Fourier transform, F {∂ α g(x)/∂|x| α } = −|k| α g(k) [95]. Setting α = 2 and x 0 = 0 we retrieve the dynamic equation obtained in [81] corresponding to Brownian motion with PSR, see also below. For 0 < c < 1 we can simplify equation ( 15) by using the partial fraction decomposition 9…”

Section: Lévy Flightsmentioning

confidence: 99%

“…In [79] the authors discussed PSR for both scenarios in terms of moments and the particle probability density function (PDF). The case of dependent resetting was recently also analysed further [80,81]. PSR finds its motivation in different settings.…”

Section: Introductionmentioning

confidence: 99%

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Time-dependent probability density function for partial resetting dynamics

et al. 2023

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Stochastic resetting is a rapidly developing topic in the field of stochasticprocesses and their applications. It denotes the occasional reset of adiffusing particle to its starting point and effects, inter alia, optimalfirst-passage times to a target. Recently the concept of partial resetting,in which the particle is reset to a given fraction of the current valueof the process, has been established and the associated search behaviouranalysed. Here we go one step further and we develop a general technique todetermine the time-dependent probability density function (PDF) for Markovprocesses with partial resetting. We obtain an exact representation of thePDF in the case of general symmetric L{'e}vy flights with stable index$0<\alpha\le2$. For Cauchy and Brownian motions (i.e., $\alpha=1,2$), thisPDF can be expressed in terms of elementary functions in positionspace. We also determine the stationary PDF. Our numerical analysis of thePDF demonstrates intricate crossover behaviours as function of time.

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