Stopping Markov processes and first path on graphs | Zendy

Giacomo Aletti | Zendy; Ely Merzbach | Zendy

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Stopping Markov processes and first path on graphs

Author(s) -

Giacomo Aletti,

Ely Merzbach

Publication year - 2006

Publication title -

journal of the european mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 3.549

H-Index - 64

eISSN - 1435-9863

pISSN - 1435-9855

DOI - 10.4171/jems/38

Subject(s) - mathematics , markov chain , stopping time , combinatorics , graph , embedding , discrete mathematics , path (computing) , markov process , markov chain mixing time , markov model , markov property , computer science , statistics , artificial intelligence , programming language

Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a non combinatorial method to compute the law of stopping. Several applied examples are presented. The problem of embedding a graph into a larger but minimal graph under some constraints is studied. Given a connected graph, we show a non combinatorial manner to compute the law of a first given path among a set of stopping paths. We prove the existence of a minimal Markov chain without oversized information.

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