Characterization of stationary states in random walks with stochastic resetting.

@article{Mndez2016CharacterizationOS,
  title={Characterization of stationary states in random walks with stochastic resetting.},
  author={Vicenç M{\'e}ndez and Daniel Campos},
  journal={Physical review. E},
  year={2016},
  volume={93 2},
  pages={
          022106
        }
}
It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump models it is shown that stationary states emerge for any shape of the waiting-time and jump length distributions. The existence of such state entails… 

Figures from this paper

Transport properties of random walks under stochastic noninstantaneous resetting.

TLDR
This work introduces noninstantaneous resetting as a two-state model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state whereThe walker performs a ballistic motion with constant velocity towards the origin.

Continuous-time random walks under power-law resetting.

TLDR
It is shown, that the behavior of the MSD is the same as in the scaled Brownian motion (SBM), being the mean-field model of the CTRW, and the intermediate asymptotics of the probability density functions for CTRW under complete resetting (provided they exist) are also the same.

Transport properties and first-arrival statistics of random motion with stochastic reset times.

TLDR
This work studies the existence of a finite equilibrium mean-square displacement (MSD) when resets are applied to random motion with 〈x^{2}(t)〉_{m}∼t^{p} for 0<p≤2}.

Symmetric exclusion process under stochastic resetting.

TLDR
While the typical fluctuations of both the diffusive and reset currents around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behavior.

Random acceleration process under stochastic resetting

  • Prashant Singh
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2020
We consider the motion of a randomly accelerated particle in one dimension under stochastic resetting mechanism. Denoting the position and velocity by x and v respectively, we consider two different

Nonrenewal resetting of scaled Brownian motion.

We investigate an intermittent stochastic process in which diffusive motion with a time-dependent diffusion coefficient, D(t)∼t^{α-1}, α>0 (scaled Brownian motion), is stochastically reset to its

Stochastic resetting and applications

In this topical review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose

Work Fluctuations and Jarzynski Equality in Stochastic Resetting.

TLDR
It is shown that the distribution function of the work typically, in asymptotic times, converges to a universal Gaussian form for any protocol as long as that is also renewed after each resetting event.

Invariants of motion with stochastic resetting and space-time coupled returns

Motion under stochastic resetting serves to model a myriad of processes in physics and beyond, but in most cases studied to date resetting to the origin was assumed to take zero time or a time

Non-linear diffusion with stochastic resetting

  • P. Chelminiak
  • Mathematics
    Journal of Physics A: Mathematical and Theoretical
  • 2022
Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a
...

References

SHOWING 1-10 OF 11 REFERENCES

ET

. — The holotype of Proctotretus signifer Dum. et Bibr., 1837, considered as lost since 1851, has been found again in the Paris Museum material that was catalogued as a type-series of P. fitzingerii

Phys

  • Rev. E 92, 062115
  • 2015

Rev

  • Mod. Phys. 83, 81
  • 2011

Phys

  • Rev. E 82, 061112
  • 2010

Phys

  • Rev. E 87, 012116
  • 2013

A: Math

  • Theor. 47, 285001
  • 2014

Phys

  • Rev. Lett. 113, 220602
  • 2014

Proc

  • Natl. Acad. Sci. USA 105, 4633
  • 2008

Phys

  • Rev. E 55, 99
  • 1997

Phys

  • Rev. E 91, 052131
  • 2015