Related papers: Capturing correlations in chaotic diffusion by app…
The foundations of the fractional diffusion equation are investigated based on coupled and decoupled continuous time random walks (CTRW). For this aim we find an exact solution of the decoupled CTRW, in terms of an infinite sum of stable…
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
We calculate the diffusion coefficient of an active tracer in a schematic crowded environment, represented as a lattice gas of passive particles with hardcore interactions. Starting from the master equation of the problem, we put forward a…
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
We derive and analyze new diffusion approximations of stationary distributions of Markov chains that are based on second- and higher-order terms in the expansion of the Markov chain generator. Our approximations achieve a higher degree of…
Rajagopalan and Sabir [nlin.CD/0104021 and Phys. Rev. E 63, 057201 (2001)] recently discussed deterministic diffusion in a piecewise linear map using an approach developed by Fujisaka et al. We first show that they rederived the random walk…
This paper concerns the propagation of particles through a quenched random medium. In the one- and two-dimensional models considered, the local dynamics is given by expanding circle maps and hyperbolic toral automorphisms, respectively. The…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
Using a numerical library for arbitrary precision arithmetic I study the irregular dependence of the diffusion coefficient on the slope of a piecewise linear map defining a dynamical system. I find that the graph of the diffusion…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
This study explores a Gaussian quasi-likelihood approach for estimating parameters of diffusion processes with Markovian regime switching. Assuming the ergodicity under high-frequency sampling, we will show the asymptotic normality of the…
Exploiting the coherent medium approximation, random walk among sites distributed randomly in space is investigated when the jump rate depends on the distance between two adjacent sites. In one dimension, it is shown that when the jump rate…
Diffusive approximations of Markov jump processes often fail to accurately capture large fluctuations. This is confounding, as the rare events triggered by these large fluctuations, such as the failure of electronic memories, are often the…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…