# Non-homogeneous random walks on a semi-infinite strip

@article{Georgiou2014NonhomogeneousRW,
title={Non-homogeneous random walks on a semi-infinite strip},
author={Nicholas Georgiou and Andrew R. Wade},
journal={Stochastic Processes and their Applications},
year={2014},
volume={124},
pages={3179-3205}
}
• Published 11 February 2014
• Mathematics
• Stochastic Processes and their Applications
We study the asymptotic behaviour of Markov chains (Xn,ηn) on Z+×S, where Z+ is the non-negative integers and S is a finite set. Neither coordinate is assumed to be Markov. We assume a moments bound on the jumps of Xn, and that, roughly speaking, ηn is close to being Markov when Xn is large. This departure from much of the literature, which assumes that ηn is itself a Markov chain, enables us to probe precisely the recurrence phase transitions by assuming asymptotically zero drift for Xn given… Expand
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#### References

SHOWING 1-10 OF 29 REFERENCES
Heavy traffic analysis of a random walk on a lattice semi-strip
We consider a Markov chain whose state space is a product of non-negative integers and a finite set. Transition probabilities satisfy certain conditions of a limited spacial homogeneity with respectExpand
RECURRENCE OF ADDITIVE FUNCTIONALS OF MARKOV CHAINS
The central problem discussed in this paper is that of deciding the recurrence or transience of 'random walk' on a regular grid in the plane, for example, the equilateral triangular grid, or theExpand
On random walks with restricted reversals
• Mathematics
• 1958
1. Introduction . Problems of unrestricted random walks on lattices have been considered by many authors and methods have been discovered for the exact enumeration of the number of walks between twoExpand
Correlated random walk
Random walk on a d-dimensional lattice is investigated such that, at any stage, the probabilities of the step being in the various possible directions depend upon the direction of the previous step.Expand
Recurrence for persistent random walks in two dimensions
We discuss the question of recurrence for persistent, or Newtonian, random walks in ℤ2, i.e. random walks whose transition probabilities depend both on the walker's position and incoming direction.Expand
Stability of a Markov-modulated Markov Chain, with Application to a Wireless Network Governed by two Protocols
• Mathematics
• 2012
We consider a discrete-time Markov chain (Xt,Yt), t = 0, 1, 2,…, where the X-component forms a Markov chain itself. Assume that (Xt) is Harris-ergodic and consider an auxiliary Markov chain {Yt}Expand
On the Recurrence Set of Planar Markov Random Walks
• Mathematics
• 2012
In this paper, we investigate properties of recurrent planar Markov random walks. More precisely, we study the set of recurrence points with the use of local limit theorems. The Nagaev–Guivarc’hExpand
XXI.—The Statistical Theory of Stiff Chains
The paper is concerned with the distributional properties of Markoff chains in two and three dimensions where the transition probability for the length of a step and its orientation relative to thatExpand
Senile reinforced random walks
• Mathematics
• 2006
We consider random walks with transition probabilities depending on the number of consecutive traversals n of the edge most recently traversed. Such walks may get stuck on a single edge, or haveExpand
Random walks with internal degrees of freedom
• Mathematics
• 1983
Between two absorbing barriers consider a random walk with a finite number of internal degrees of freedom and with zero drift. By using a functional-analytic approach based on the spectral theory ofExpand