Connecting irreducible and absorbing Markov chains - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2023

Connecting irreducible and absorbing Markov chains

Abstract

This talk is about connections between irreducible and absorbing Markov chains. One of those connections is using Sigmund duality theory. In the talk, we will describe a more direct way of associating the two classes of processes, allowing to evaluate important quantities defined in one of the chains by calculating on the other one. Using this connection, we will focus on a specific application of previous result, the derivation of relations in the absorbing process similar to equilibrium through cuts operating on the corresponding irreducible chain. These relations provide equilibrium equations allowing to obtain more easily quantities associated with the process in equilibrium. In the absorbing case, the corresponding relations connect mean sojourn times in the transient states until absorption. We will illustrate them with simple examples using both finite and infinite absorbing processes.
Fichier principal
Vignette du fichier
sl-irredAbs-Apr23.pdf (295.9 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04381185 , version 1 (09-01-2024)

Licence

Public Domain

Identifiers

  • HAL Id : hal-04381185 , version 1

Cite

Gerardo Rubino. Connecting irreducible and absorbing Markov chains. AMS Spring Eastern Sectional Meeting 2023, AMS, Apr 2023, Virtual conference, United States. ⟨hal-04381185⟩
6 View
3 Download

Share

Gmail Facebook X LinkedIn More