Generalized martingales, generalized Markov chains and generalized harmonic functions

1988 ◽  
Vol 79 (3) ◽  
pp. 405-430
Author(s):  
Louis H. Blake
Keyword(s):  
Markov Chains ◽  
Harmonic Functions ◽  
Generalized Harmonic Functions

scholarly journals Harmonic functions for a class of Markov chains

1979 ◽  
Vol 28 (4) ◽  
pp. 413-422 ◽  
Author(s):  
H. Cohn
Keyword(s):  
Markov Chains ◽  
Harmonic Functions ◽  
Branching Process ◽  
Space Time ◽  
Time Harmonic ◽  
Bounded Space ◽  
Tail Events ◽  
Bounded Harmonic Functions

AbstractA class of Markov chains is considered for which a certain property of the tail events makes bounded harmonic functions obtainable from bounded space-time harmonic functions. Applications to almost surely convergent Markov chains are given and, in particular, a representation of Martin-Doob-Hunt type is derived for all bounded harmonic functions of a finite mean supercritical branching process.

FURSTENBERG-TYPE FORMULAS OVER SHIFT SPACES

2003 ◽  
Vol 03 (04) ◽  
pp. 499-527
Author(s):  
SUSANNE KOCH
Keyword(s):  
Markov Chains ◽  
Integral Representation ◽  
Harmonic Functions ◽  
Type Formula ◽  
Shift Spaces ◽  
Type Integral ◽  
Self Similar

We define a class of Markov chains of unbounded range on word spaces and deduce a Furstenberg-type integral representation for a subspace of the P-harmonic functions. As an application we obtain a Furstenberg-type formula for a set of continuous harmonic functions on p.c.f. self-similar sets.

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