2022
DOI: 10.48550/arxiv.2204.07215
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An advection-diffusion process with proportional resetting

Abstract: This paper presents a diffusion process with a novel resetting mechanism in which the amplitude of the process is instantaneously converted to a proportion of its value at random times. This model is described by a Langevin equation with both additive Gaussian white noise and multiplicative Poisson shot noise terms. The distribution function obeys a pantograph equation, a functional partial differential equation evaluated at two amplitudes simultaneously. From this equation the exact statistical moments and st… Show more

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Cited by 3 publications
(9 citation statements)
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References 54 publications
(89 reference statements)
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“…In the limiting case α = 2 we obtain the same result as in [80,81]. Alternatively, we could have obtained this result by taking the limit lim s→0 s pr (k, s|x 0 ) in equation ( 16).…”
Section: Stationary Distributionsupporting
confidence: 72%
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“…In the limiting case α = 2 we obtain the same result as in [80,81]. Alternatively, we could have obtained this result by taking the limit lim s→0 s pr (k, s|x 0 ) in equation ( 16).…”
Section: Stationary Distributionsupporting
confidence: 72%
“…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%
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