Superdiffusion of a random walk driven by an ergodic Markov process with switching
نویسندگان
چکیده
We propose a Markov model with an ergodic two-component switching mechanism that dynamically generates anomalous diffusion. The first component plays the role of a hidden parameter. The second one is the switching component generating the superdiffusion of a random walker and is itself non-Markovian. The model is studied numerically using the Monte Carlo technique. PACS numbers: 05.40.Fb, 02.50.Ga, 05.10.Gg Mathematics Subject Classification: 60J27, 60K35, 60K40, 60G35
منابع مشابه
A PRELUDE TO THE THEORY OF RANDOM WALKS IN RANDOM ENVIRONMENTS
A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...
متن کاملTotal Variation Discrepancy of Deterministic Random Walks for Ergodic Markov Chains
Motivated by a derandomization of Markov chain Monte Carlo (MCMC), this paper investigates deterministic random walks, which is a deterministic process analogous to a random walk. While there are several progresses on the analysis of the vertex-wise discrepancy (i.e., L∞ discrepancy), little is known about the total variation discrepancy (i.e., L1 discrepancy), which plays a significant role in...
متن کاملStability and approximation of invariant measures of Markov chains in random environments
We consider finite-state Markov chains driven by stationary ergodic invertible processes representing random environments. Our main result is that the invariant measures of Markov chains in random environments (MCREs) are stable under a wide variety of perturbations. We prove stability in the sense of convergence in probability of the invariant measure of the perturbed MCRE to the original inva...
متن کاملPersistent random walk of cells involving anomalous effects and random death.
The purpose of this paper is to implement a random death process into a persistent random walk model which produces sub-ballistic superdiffusion (Lévy walk). We develop a stochastic two-velocity jump model of cell motility for which the switching rate depends upon the time which the cell has spent moving in one direction. It is assumed that the switching rate is a decreasing function of residen...
متن کاملCutoff Phenomenon for Random Walks on Kneser Graphs
The cutoff phenomenon for an ergodic Markov chain describes a sharp transition in the convergence to its stationary distribution, over a negligible period of time, known as cutoff window. We study the cutoff phenomenon for simple random walks on Kneser graphs, which is a family of ergodic Markov chains. Given two integers n and k, the Kneser graph K(2n+ k, n) is defined as the graph with vertex...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007