On large deviations of Markov processes with discontinuous statistics

On Large Deviations of Markov Processes 1 with Discontinuous

This paper establishes a process-level large deviations principle for Markov processes in the Euclidean space with a discontinuity in the transition mechanism along a hyper-plane. The transition mechanism of the process is assumed to be continuous on one closed halfspace, and also continuous on the complementary open halfspace. Similar results were recently obtained for discrete time processes ...

Nonequilibrium Markov Processes Conditioned on Large Deviations

Martingale Problems for Large Deviations of Markov Processes

The martingale problems provide a powerful tool for characterizing Markov processes, especially in addressing convergence issues. For each n, let metric space E-valued process X n be a solution of the A n martingale problems (i.e. f (X n (t)) ? f (X n (0)) ? Z t 0 A n f (X n (s))ds is a martingale), the convergence of A n f ! Af in some sense usually implies the weak convergence of X n) X , whe...

Large Deviations Bounds for Markov Decision Processes Under General Policies

We consider the empirical state-action frequencies and the empirical reward in weakly communicating finite-state Markov decision processes under general policies. We define a certain polytope and establish that every element of this polytope is the limit of the empirical frequency vector, under some policy, in a strong sense. Furthermore, we show that the probability of exceeding a given distan...

Large Deviations for Occupation Measures for Markov Processes

A simple proof of Donsker-Varadhan’s large deviation principle (LDP) for occupation measure of Markov process, valued in R, with the discrete time is given. A proof is based on a new version of Dupui-Ellis’s large deviation principle for two-dimensional occupation measures. In our setting, an existence of the invariant measure does not assumed. This condition is replaced (from point of view of ...