Stopping Markov processes and first path on graphs

Giacomo Aletti, Ely Merzbach

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Given a strongly stationary Markov chain (discrete or continuous) and a finite set of stopping rules, we show a noncombinatorial method to compute the law of stopping. Several 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 noncombinatorial 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.

Original languageEnglish
Pages (from-to)49-75
Number of pages27
JournalJournal of the European Mathematical Society
Issue number1
StatePublished - 2006


  • Directed graph
  • Markov chains
  • Stopping rules


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