A Comparison of Random Walks in Dependent Random Environments
نویسندگان
چکیده
Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the actual evaluation of various characteristics of such processes has received relatively little attention. This paper develops new methodology for the exact computation of the drift in such models. Focusing on random walks in dependent random environments, including k-dependent and moving average environments, we show how the drift can be characterized and found using Perron-Frobenius theory. We compare random walks in various dependent environments and show that their drift behavior can differ significantly. MSC subject classifications: Primary 60K37, 60G50; secondary 82B41
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 کاملComputing the Drift of Random Walks in Dependent Random Environments
Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops new theory and methodology for the computation of the drift of the random walk for various dependent random environments, including k-dependent and moving a...
متن کاملLimit Theory for Random Walks in Degenerate Time-dependent Random Environments
We study continuous-time (variable speed) random walks in random environments on Zd , d≥ 2, where, at time t, the walk at x jumps across edge (x,y) at time-dependent rate at(x,y). The rates, which we assume stationary and ergodic with respect to space-time shifts, are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite interva...
متن کاملGaussian fluctuations for random walks in random mixing environments
We consider a class of ballistic, multidimensional random walks in random environments where the environment satisfies appropriate mixing conditions. Continuing our previous work [2] for the law of large numbers, we prove here that the fluctuations are gaussian when the environment is Gibbsian satisfying the “strong mixing condition” of Dobrushin and Shlosman and the mixing rate is large enough...
متن کاملOne-dimensional linear recursions with Markov-dependent coefficients
For a class of stationary Markov-dependent sequences (ξn, ρn) ∈ R 2, we consider the random linear recursion Sn = ξn + ρnSn−1, n ∈ Z, and show that the distribution tail of its stationary solution has a power law decay. An application to random walks in random environments is discussed. MSC2000: primary 60K15 ; secondary 60K20, 60K37.
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 2015