# Stopping Markov processes and first path on graphs

### Giacomo Aletti

Università degli Studi di Milano, Italy### Ely Merzbach

Bar-Ilan University, Ramat-Gan, Israel

## Abstract

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.

## Cite this article

Giacomo Aletti, Ely Merzbach, Stopping Markov processes and first path on graphs. J. Eur. Math. Soc. 8 (2006), no. 1, pp. 49–75

DOI 10.4171/JEMS/38