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The standard Levy walk is performed by a particle that moves ballistically between randomly occurring collisions, when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events…

Statistical Mechanics · Physics 2012-04-03 S. Denisov , V. Zaburdaev , P. Hanggi

In this paper, we consider a stochastic process that may experience random reset events which relocate the system to its starting position. We focus our attention on a one-dimensional, monotonic continuous-time random walk with a constant…

Mathematical Physics · Physics 2017-10-11 Miquel Montero , Axel Masó-Puigdellosas , Javier Villarroel

We consider a generalization of a one-dimensional stochastic process known in the physical literature as L\'evy-Lorentz gas. The process describes the motion of a particle on the real line in the presence of a random array of marked points,…

Probability · Mathematics 2016-04-12 Alessandra Bianchi , Giampaolo Cristadoro , Marco Lenci , Marilena Ligabò

Resetting a stochastic process is an important problem describing the evolution of physical, biological and other systems which are continually returned to their certain fixed point. We consider the motion of a subdiffusive particle with a…

Statistical Mechanics · Physics 2024-01-18 Aleksander A. Stanislavsky

One of the characteristic features of a stochastic process under resetting is that the probability density converges to a nonequilibrium stationary state (NESS). In addition, the approach to the stationary state exhibits a dynamical phase…

Statistical Mechanics · Physics 2021-09-01 Paul C Bressloff

Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…

Statistical Mechanics · Physics 2016-03-23 Stephan Eule , Jakob Metzger

We consider stochastic systems involving general -- non-Gaussian and asymmetric -- stable processes. The random quantities, either a stochastic force or a waiting time in a random walk process, explicitly depend on the position. A…

Statistical Mechanics · Physics 2015-06-18 Tomasz Srokowski

Continuous time random walks combining diffusive and ballistic regimes are introduced to describe a class of L\'evy walks on lattices. By including exponentially-distributed waiting times separating the successive jump events of a walker,…

Statistical Mechanics · Physics 2014-12-02 Giampaolo Cristadoro , Thomas Gilbert , Marco Lenci , David P. Sanders

Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…

Statistical Mechanics · Physics 2021-10-27 Santanu Das , Anupam Kundu

The discrete stochastic dynamics of a random walker in the presence of resetting and memory is analyzed. Resetting and memory effects may compete for certain parameter regime and lead to significant changes in the long time dynamics of the…

Statistical Mechanics · Physics 2023-11-15 Upendra Harbola

In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…

Statistical Mechanics · Physics 2020-12-08 Carlos A. Plata , Deepak Gupta , Sandro Azaele

Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce non-instantaneous resetting as a two-state model being a combination of an exploring…

Statistical Mechanics · Physics 2019-10-23 Axel Masó-Puigdellosas , Daniel Campos , Vicenç Méndez

We investigate an intermittent stochastic process, in which the diffusive motion with time-dependent diffusion coefficient $D(t)\sim t^{\alpha-1}$, $\alpha>0$ (scaled Brownian motion), is stochastically reset to its initial position and…

Statistical Mechanics · Physics 2019-07-24 Anna S. Bodrova , Aleksei V. Chechkin , Igor M. Sokolov

We study a $d$-dimensional stochastic process $\mathbf{X}$ which arises from a L\'evy process $\mathbf{Y}$ by partial resetting, that is the position of the process $\mathbf{X}$ at a Poisson moment equals $c$ times its position right before…

Probability · Mathematics 2024-12-23 Tomasz Grzywny , Karol Szczypkowski , Zbigniew Palmowski , Bartosz Trojan

Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…

Soft Condensed Matter · Physics 2025-10-30 Agniva Datta , Carsten Beta , Robert Großmann

We consider the simple random walk (or P\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers…

Probability · Mathematics 2024-01-04 Claude Godrèche , Jean-Marc Luck

The aim of this paper is to analyze a class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction. The speed randomly changes when a Poissonian event occurs.…

Probability · Mathematics 2009-12-31 Alessandro De Gregorio

We study the effects of stochastic resetting on geometric Brownian motion (GBM), a canonical stochastic multiplicative process for non-stationary and non-ergodic dynamics. Resetting is a sudden interruption of a process, which consecutively…

Risk Management · Quantitative Finance 2021-08-24 Viktor Stojkoski , Trifce Sandev , Ljupco Kocarev , Arnab Pal

We compute the average shape of trajectories of some one--dimensional stochastic processes x(t) in the (t,x) plane during an excursion, i.e. between two successive returns to a reference value, finding that it obeys a scaling form. For…

Statistical Mechanics · Physics 2009-11-10 Francesca Colaiori , Andrea Baldassarri , Claudio Castellano

Almost all the media the particles move in are non-static. Depending on the expected resolution of the studied dynamics and the amplitude of the displacement of the media, sometimes the non-static behaviours of the media can not be ignored.…

Statistical Mechanics · Physics 2022-01-05 Tian Zhou , Pengbo Xu , Weihua Deng