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In a recent work we introduced a semi-Markovian discrete-time generalization of the telegraph process. We referred this random walk to as squirrel random walk (SRW). The SRW is a discrete-time random walk on the one-dimensional infinite…

Probability · Mathematics 2023-01-18 Thomas M. Michelitsch , Federico Polito , Alejandro P. Riascos

The usual development of the continuous-time random walk (CTRW) proceeds by assuming that the present is one of the jumping times. Under this restrictive assumption integral equations for the propagator and mean escape times have been…

Statistical Finance · Quantitative Finance 2009-07-17 Javier Villarroel , Miquel Montero

In this paper we study the behavior of a continuous time random walk (CTRW) on a stationary and ergodic time varying dynamic graph. We establish conditions under which the CTRW is a stationary and ergodic process. In general, the stationary…

Social and Information Networks · Computer Science 2012-12-04 Daniel Figueiredo , Philippe Nain , Bruno Ribeiro , Edmundo de Souza e Silva , Don Towsley

Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous…

Probability · Mathematics 2011-10-04 Meredith N. Burr

Continuous Time Random Walks (CTRWs) are jump processes with random waiting times between jumps. We study scaling limits for CTRWs where the distribution of jumps and waiting times is coupled and varies in space and time. Such processes…

Probability · Mathematics 2015-01-06 Peter Straka

We show that for a weakly dense subset of the domain of attraction of a positive stable random variable of index $0<\alpha<1$($DOA\left(\alpha\right))$ the functional stable convergence is a time-changed renewal convergence of distribution…

Probability · Mathematics 2017-09-12 Ofer Busani

Correlated random walks (CRW) have been used for a long time as a null model for animal's random search movement in two dimensions (2D). An increasing number of studies focus on animals' movement in three dimensions (3D), but the key…

Other Quantitative Biology · Quantitative Biology 2019-01-11 Simon Benhamou

We consider Brownian motion under resetting in higher dimensions for the case when the return of the particle to the origin occurs at a constant speed. We investigate the behavior of the probability density function (PDF) and of the…

Statistical Mechanics · Physics 2020-09-23 Anna S. Bodrova , Igor M. Sokolov

Continuous-time random walks (CTRWs) on discrete state spaces, ranging from regular lattices to complex networks, are ubiquitous across physics, chemistry, and biology. Models with coarse-grained states, for example those employed in…

Statistical Mechanics · Physics 2015-12-03 Michael Manhart , Willow Kion-Crosby , Alexandre V. Morozov

The concept of continuous-time random walks (CTRW) is a generalization of ordinary random walk models, and it is a powerful tool for investigating a broad spectrum of phenomena in natural, engineering, social and economic sciences.…

Statistical Mechanics · Physics 2015-06-12 Hamid Teimouri , Anatoly B. Kolomeisky

We derive the characteristic function of stochastic functionals of a random walk whose position is reset to the origin at random times drawn from a general probability distribution. We analyze the long-time behavior and obtain the temporal…

Statistical Mechanics · Physics 2025-07-09 V. Méndez , R. Flaquer-Galmés

The usual development of the continuous time random walk (CTRW) assumes that jumps and time intervals are a two-dimensional set of independent and identically distributed random variables. In this paper we address the theoretical setting of…

Data Analysis, Statistics and Probability · Physics 2008-09-29 Miquel Montero , Jaume Masoliver

Based on the theory of continuous time random walks (CTRW), we build the models of characterizing the transitions among anomalous diffusions with different diffusion exponents, often observed in natural world. In the CTRW framework, we take…

Statistical Mechanics · Physics 2018-09-13 Trifce Sandev , Weihua Deng , Pengbo Xu

We investigate aging continuous time random walks (ACTRW), introduced by Monthus and Bouchaud [{\em J. Phys. A} {\bf 29}, 3847 (1996)]. Statistical behaviors of the displacement of the random walker ${\bf r}={\bf r}(t) - {\bf r}(0)$ in the…

Statistical Mechanics · Physics 2009-11-07 Eli Barkai , Yuan-Chung Cheng

The effects of spatial confinements and smooth cutoffs of the waiting time distribution in continuous-time random walks (CTRWs) are studied analytically. We also investigate dependences of ergodic properties on initial ensembles (i.e.,…

Statistical Mechanics · Physics 2013-03-27 Tomoshige Miyaguchi , Takuma Akimoto

Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their…

Probability · Mathematics 2014-07-25 Mark M. Meerschaert , Peter Straka

We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time…

Statistical Mechanics · Physics 2022-05-25 Vicenç Méndez , Axel Masó-Puigdellosas , Daniel Campos

We study ultraslow diffusion processes with logarithmic mean squared displacement (MSD) $\langle x^2(t)\rangle\simeq\log^{\gamma}t$. Comparison of annealed continuous time random walks (CTRWs) with logarithmic waiting time distribution…

Statistical Mechanics · Physics 2014-12-24 Aljaz Godec , Aleksei V. Chechkin , Eli Barkai , Holger Kantz , Ralf Metzler

The continuous-time random walk (CTRW) model is useful for alleviating the computational burden of simulating diffusion in actual media. In principle, isotropic CTRW only requires knowledge of the step-size, $P_l$, and waiting-time, $P_t$,…

Statistical Mechanics · Physics 2017-01-19 Shahar Amitai , Raphael Blumenfeld

We study the joint action of the non-Poisson renewal events (NPR) yielding Continuous Time Random Walk (CTRW) with index alpha < 1 and two different generators of Hurst coefficient H not equal to 0.5, one generating fractional Brownian…

Statistical Mechanics · Physics 2016-08-03 Elvis Geneston , Rohisha Tuladhar , M. T. Beig , Mauro Bologna , Paolo Grigolini