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We study continuous time random walks (CTRW) with power law distribution of waiting times under resetting which brings the walker back to the origin, with a power-law distribution of times between the resetting events. Two situations are…

Statistical Mechanics · Physics 2020-07-01 Anna S. Bodrova , Igor M. Sokolov

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

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

There exist important stochastic physical processes involving infinite mean waiting times. The mean divergence has dramatic consequences on the process dynamics. Fractal time random walks, a diffusion process, and subrecoil laser cooling, a…

Disordered Systems and Neural Networks · Physics 2015-06-24 F. Bardou

In this article, we generalize the recent Discrete Time Random Walk (DTRW) algorithm, which was introduced for the computation of probability densities of fractional diffusion. Although it has the same computational complexity and shares…

Computational Physics · Physics 2018-08-20 Gurtek Gill , Peter Straka

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Levy alpha-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the…

Statistical Mechanics · Physics 2013-03-19 Daniel Fulger , Enrico Scalas , Guido Germano

We analyze generalized space-time fractional motions on undirected networks and lattices. The continuous-time random walk (CTRW) approach of Montroll and Weiss is employed to subordinate a space fractional walk to a generalization of the…

The uncoupled Continuous Time Random Walk (CTRW) in one space-dimension and under power law regime is splitted into three distinct random walks: (rw_1), a random walk along the line of natural time, happening in operational time; (rw_2), a…

Probability · Mathematics 2011-04-21 Rudolf Gorenflo , Francesco Mainardi

Superslow diffusion, i.e., the long-time diffusion of particles whose mean-square displacement (variance) grows slower than any power of time, is studied in the framework of the decoupled continuous-time random walk model. We show that this…

Statistical Mechanics · Physics 2010-11-24 S. I. Denisov , H. Kantz

We demonstrate that continuous time random walks in which successive waiting times are correlated by Gaussian statistics lead to anomalous diffusion with mean squared displacement <r^2(t)>~t^{2/3}. Long-ranged correlations of the waiting…

Statistical Mechanics · Physics 2015-05-14 Vincent Tejedor , Ralf Metzler

In this paper, we consider an age-structured jump model that arises as a description of continuous time random walks with infinite mean waiting time between jumps. We prove that under a suitable rescaling, this equation converges in the…

Analysis of PDEs · Mathematics 2026-01-14 Hugues Berry , Pierre Gabriel , Thomas Lepoutre , Nathan Quiblier

We discuss large deviation properties of continuous-time random walks (CTRW) and present a general expression for the large deviation rate in CTRW in terms of the corresponding rates for the distributions of steps' lengths and waiting…

Statistical Mechanics · Physics 2021-04-14 Adrian Pacheco-Pozo , Igor M. Sokolov

Continuous time random walks (CTRWs) are used in physics to model anomalous diffusion, by incorporating a random waiting time between particle jumps. In finance, the particle jumps are log-returns and the waiting times measure delay between…

Data Analysis, Statistics and Probability · Physics 2008-12-10 Mark M. Meerschaert , Enrico Scalas

The three-dimensional (3D) Fick's diffusion equation and fractional diffusion equation are solved for different reflecting boundaries. We use the continuous time random walk model (CTRW) to investigate the time averaged mean square…

Soft Condensed Matter · Physics 2017-09-25 Shanlin Qin , Yong He

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

Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…

Statistical Mechanics · Physics 2017-12-05 Liang Luo , Lei-Han Tang

In this paper, we consider a type of continuous time random walk model where the jump length is correlated with the waiting time. The asymptotic behaviors of the coupled jump probability density function in the Fourier-Laplace domain are…

Statistical Mechanics · Physics 2015-06-16 Long Shi , Zuguo Yu , Zhi Mao , Aiguo Xiao , Hailan Huang

We consider the dynamics of a separable Continuous Time Random Walk (CTRW) when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid…

Statistical Mechanics · Physics 2020-08-26 F. Le Vot , E. Abad , R. Metzler , S. B. Yuste

The first-return time is the time that it takes a random walker to go back to the initial position for the first time. We study the first-return time when random walkers perform fractional kinetics, specifically fractional diffusion, that…

Statistical Mechanics · Physics 2026-03-17 M. Dahlenburg G. Pagnini

The main purpose of this note is to point out the relevance of the Mittag-Leffler probability distribution in the so-called thinning theory for a renewal process with a queue of power law type. This theory, formerly considered by Gnedenko…

Probability · Mathematics 2018-08-21 Rudolf Gorenflo , Francesco Mainardi