@inbook{a3c97163c09b434581b8f7371b6a8b5b,
title = "Martingales, Harmonic Functions and Poisson{\textendash}Dirichlet Problems",
abstract = "In this chapter, we introduce several notions of potential theory for Markov chains. Harmonic and superharmonic functions on a set A are defined in Section 4.1, and Theorem 4.1.3 establishes links between these functions and the return (or hitting) times to the set A. In Section 4.2, we introduce the potential kernel and prove the maximum principle, Theorem 4.2.2, which will be very important in the study of recurrence and transience throughout Part II.",
author = "Randal Douc and Eric Moulines and Pierre Priouret and Philippe Soulier",
note = "Publisher Copyright: {\textcopyright} 2018, Springer Nature Switzerland AG.",
year = "2018",
month = jan,
day = "1",
doi = "10.1007/978-3-319-97704-1\_4",
language = "English",
series = "Springer Series in Operations Research and Financial Engineering",
publisher = "Springer Nature",
pages = "75--96",
booktitle = "Springer Series in Operations Research and Financial Engineering",
}