scholarly journals On σ-Finite Measures Related to the Martin Boundary of Recurrent Markov Chains

2015 ◽  
pp. 263-297 ◽  
Author(s):  
Joseph Najnudel
Keyword(s):  
Markov Chains ◽  
Martin Boundary ◽  
Finite Measures

scholarly journals On the asymptotic events of a Markov chain

1979 ◽  
Vol 2 (4) ◽  
pp. 537-587 ◽  
Author(s):  
Harry Cohn
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Martin Boundary ◽  
Boundary Theory ◽  
Unified Approach ◽  
Nonhomogeneous Markov Chains ◽  
Structure Properties

In this paper we investigate some structure properties of the tailσ-field and the invariantσ-field of both homogeneous and nonhomogeneous Markov chains as representations for asymptotic events, descriptions of completely nonatomic and atomic sets and global characterizations of asymptoticσ-fields. It is shown that the Martin boundary theory can provide a unified approach to the asymptoticσ-fields theory.

scholarly journals Martin boundaries of cartesian products of markov chains

1992 ◽  
Vol 128 ◽  
pp. 153-169 ◽  
Author(s):  
Massimo A. Picardello ◽  
Wolfgang Woess
Keyword(s):  
Markov Chains ◽  
Harmonic Functions ◽  
Cartesian Product ◽  
Martin Boundary ◽  
State Spaces ◽  
Cartesian Products ◽  
Discrete State ◽  
Stochastic Transition ◽  
Transition Operators ◽  
Martin Boundaries

Let P and Q be the stochastic transition operators of two time-homogeneous, irreducible Markov chains with countable, discrete state spaces X and Y, respectively. On the Cartesian product Z = X x Y, define a transition operator of the form Ra = a·P + (1 — a) · Q, 0 < a < 1, where P is considered to act on the first variable and Q on the second. The principal purpose of this paper is to describe the minimal Martin boundary of Ra (consisting of the minimal positive eigenfunctions of Ra with respect to some eigenvalue t, also called t-harmonic functions) in terms of the minimal Martin boundaries of P and Q.

FRACTAL DIMENSIONS AND MARTIN BOUNDARY OF GRAPHS

2001 ◽  
Vol 37 (1-2) ◽  
pp. 145-167
Author(s):  
A. Telcs
Keyword(s):  
Markov Chains ◽  
Large Deviation ◽  
Fractal Dimensions ◽  
Martin Boundary ◽  
Large Deviation Theorem

This pap r shows large deviation theorem for Markov chains with spatial symmetric Gr n ’s function.Spatial symm try and behaviour of the Martin boundary is inv stigat d.

Markov models—Markov chains

2019 ◽  
Vol 16 (8) ◽  
pp. 663-664 ◽  
Author(s):  
Jasleen K. Grewal ◽  
Martin Krzywinski ◽  
Naomi Altman
Keyword(s):  
Markov Chains ◽  
Markov Models
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