This article is cited in 5 papers

Short Communications

Contractive approximations for the Varadhan's function on a finite Markov chain

R. Cavazos-Cadena^a, D. Hernández-Hernández<sup>b

a</sup> Departamento de Estadistica y Cálculo, Universidad Autónoma Agraria Narro
^b Center for Mathematical Research

Abstract: This work concerns Markov chains with finite state space. Given a real-valued cost function on the state space, the corresponding Varadhan's function, measuring the exponential growth rate of the aggregated costs, is characterized as the unique limit of the fixed points of a family of contraction operators, a conclusion that does not involve any condition on the transition law.

Keywords: risk-sensitive average cost, decreasing function along trajectories, Poisson equation, closed set.

Received: 03.02.2004
Revised: 08.11.2005

Language: English

DOI: 10.4213/tvp182

 English version: Theory of Probability and its Applications, 2008, 52:2, 315–323

Bibliographic databases:

• 
• 
• 
• 
•