First passage in discrete-time absorbing Markov chains under stochastic resetting

Chen, Hanshuang; Li, Guofeng; Huang, Feng

doi:10.48550/arxiv.2111.01330

Cited by 3 publications

(3 citation statements)

References 59 publications

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“…The usefulness of this 'restart criterion' was demonstrated in many different contexts such as diffusive systems [26,[147][148][149][150][151][152][153][154][155][156][157][158][159][160][161][162], active cellular transport [163], transport in networks [164][165][166][167][168], nonlinear deterministic systems [169], intermittent search processes [87], and the random acceleration process [170]. Below, we turn to the broader implications of equation (11).…”

Section: First Passage Under Restartmentioning

confidence: 99%

The inspection paradox in stochastic resetting

Pal

Kostinski

Reuveni

2022

J. Phys. A: Math. Theor.

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The remaining travel time of a plane shortens with every minute that passes from its departure, and a ﬂame diminishes a candle with every second it burns. Such everyday occurrences bias us to think that processes which have already begun will end before those which have just started. Yet, the inspection paradox teaches us that the converse can also happen when randomness is at play. The paradox comes from probability theory, where it is often illustrated by measuring how long passengers wait upon arriving at a bus stop at a random time. Interestingly, such passengers may on average wait longer than the mean time between bus arrivals – a counter-intuitive result, since one expects to wait less when coming some time after the previous bus departed. In this viewpoint, we review the inspection paradox and its origins. The insight gained is then used to explain why, in some situations, stochastic resetting expedites the completion of random processes. Importantly, this is done with elementary mathematical tools which help develop a probabilistic intuition for stochastic resetting and how it works. This viewpoint can thus be used as an accessible introduction to the subject.

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Section: First Passage Under Restartmentioning

confidence: 99%

The inspection paradox in stochastic resetting

Pal

Kostinski

Reuveni

2022

J. Phys. A: Math. Theor.

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“…In particular, note that for n = 0, one has A 0 (x 0 ) = t f which is nothing but the first-passage time of diffusion with resetting. The topic has been studied quite extensively spanning different stochastic processes that undergo resetting [38,[84][85][86][87][88][89][90][91][92][93]. However, to the best of our knowledge, the n = 0 cases have not yet been studied.…”

Section: Functional Of the Formmentioning

confidence: 99%

First-passage Brownian functionals with stochastic resetting

Singh

Pal

2022

J. Phys. A: Math. Theor.

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We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A first-passage functional is defined as $V=\int_0^{t_f} Z[x(\tau)]$ where $t_f$ is the first-passage time of a reset Brownian process $x(\tau)$, i.e., the first time the process crosses zero. In here, the particle is reset to $x_R>0$ at a constant rate $r$ starting from $x_0>0$ and we focus on the following functionals: (i) local time $T_{loc} = \int _0^{t_f}d \tau ~ \delta (x-x_R)$, (ii) residence time $T_{res} = \int _0^{t_f} d \tau ~\theta (x-x_R)$, and (iii) functionals of the form $A_n = \int _{0}^{t_f} d \tau [x(\tau)]^n $ with $n >-2$. For first two functionals, we analytically derive the exact expressions for the moments and distributions. Interestingly, the residence time moments reach minima at some optimal resetting rates. A similar phenomena is also observed for the moments of the functional $A_n$. Finally, we show that the distribution of $A_n$ for large $A_n$ decays exponentially as $\sim \text{exp}\left( -A_n/a_n\right)$ for all values of $n$ and the corresponding decay length $a_n$ is also estimated. In particular, exact distribution for the first passage time under resetting (which corresponds to the $n=0$ case) is derived and shown to be exponential at large time limit in accordance with the generic observation. This behavioural drift from the underlying process can be understood as a ramification due to the resetting mechanism which curtails the undesired long Brownian first passage trajectories and leads to an accelerated completion. We confirm our results to high precision by numerical simulations.

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“…In particular, note that for n = 0, one has A 0 (x 0 ) = t f which is nothing but the firstpassage time of diffusion with resetting. The topic has been studied quite extensively spanning different stochastic processes that undergo resetting [36,[79][80][81][82][83][84][85][86][87][88]. However, to the best of our knowledge, the n = 0 cases have not yet been studied.…”

Section: Functional Of the Formmentioning

confidence: 99%

First-passage Brownian functionals with stochastic resetting

Singh,

Pal

2022

Preprint

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We study the statistical properties of first-passage time functionals of a one dimensional Brownian motion in the presence of stochastic resetting. A firstpassage functional is defined aswhere t f is the first-passage time of a reset Brownian process x(τ ), i.e., the first time the process crosses zero. In here, the particle is reset to x R > 0 at a constant rate r starting from x 0 > 0 and we focus on the following functionals:, and (iii) functionals of the form A n = ´tf 0 dτ [x(τ )] n with n > −2. For first two functionals, we analytically derive the exact expressions for the moments and distributions. Interestingly, the residence time moments reach minima at some optimal resetting rates. A similar phenomena is also observed for the moments of the functional A n . Finally, we show that the distribution of A n for large A n decays exponentially as ∼ exp (−A n /a n ) for all values of n and the corresponding decay length a n is also estimated. In particular, exact distribution for the first passage time under resetting (which corresponds to the n = 0 case) is derived and shown to be exponential at large time limit in accordance with the generic observation. This behavioural drift from the underlying process can be understood as a ramification due to the resetting mechanism which curtails the undesired long Brownian first passage trajectories and leads to an accelerated completion. We confirm our results to high precision by numerical simulations.

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First passage in discrete-time absorbing Markov chains under stochastic resetting

Cited by 3 publications

References 59 publications

The inspection paradox in stochastic resetting

The inspection paradox in stochastic resetting

First-passage Brownian functionals with stochastic resetting

First-passage Brownian functionals with stochastic resetting

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