Analysis of the Large Deviations Rate Functions for the Finite-Dimensional Marginal Distributions of Cumulated I.I.D. Continuous-Time Markov Chains

Kurt Majewski

2011, v.17, №1, 49-90

ABSTRACT

The empirical distributions of an increasing number of i.i.d. continuous-time finite-state Markov processes at a finite number of time points satisfy a large deviation principle. Similarly the cumulative state occupation time distributions for these time points satisfy a large deviation principle. In this work we analyze the rate function which arises in a combination of these large deviation principles. We obtain an explicit characterization for its finiteness and a representation of its finite values by finite solutions of convex minimization problems.

Keywords: Markov chain,large deviation principle,rate function,moment generating function,decomposition,convex minimization problem