The Sample Path Large Deviations Rate Function of Cumulated I.I.D. Continuous-Time Markov Chains

#### Kurt Majewski

2011, v.17, Issue 4, 581-618

ABSTRACT

The empirical distribution of an increasing number of i.i.d. continuous-time finite-state Markov processes satisfies a sample path large deviation principle. This implies a sample path large deviation principle for the state occupation time distribution development via the contraction principle. In this work we analyze the rate function which arises in a combination of these large deviation principles. We characterize minimizing paths with fixed values at a number of given time points and show their uniqueness. We obtain an integral representation of the rate function.

Keywords: Markov chain,large deviation principle,minimizing path,integral representation,variational problem