On sigma-finite measures related to the Martin boundary of recurrent Markov chains

2014/11/07 by Joseph Najnudel, Najnudel, Joseph
Computer Science · Mathematics · #60J10 #60J45 #60J50 #60J55 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1411.2024

openalex publication_date 2014/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In our monograph with B. Roynette and M. Yor, we construct a sigma-finite measure related to penalisations of different stochastic processes, including the Brownian motion in dimension 1 or 2, and a large class of linear diffusions. In the last chapter of the monograph, we define similar measures from recurrent Markov chains satisfying some technical conditions. In the present paper, we give a classification of these measures, in function of the minimal Martin boundary of the Markov chain considered at the beginning. We apply this classification to the examples considered at the end of our monograph.

Related

• On some properties of a universal sigma-finite measure associated with a remarkable class of submartingales
• On penalisation results related with a remarkable class of submartingales
• A new construction of the σ-finite measures associated with submartingales of class (Σ)
• A remarkable σ-finite measure associated with last passage times and penalisation problems
• On some universal sigma finite measures and some extensions of Doob's optional stopping theorem