Large Deviations Principle for a Large Class of One-Dimensional Markov Processes

Accelerated decomposition techniques for large discounted Markov decision processes

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...

Nonequilibrium Markov Processes Conditioned on Large Deviations

Large Deviations for a Class of Nonhomogeneous Markov Chains

Large deviation results are given for a class of perturbed non-homogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {Pn} be a sequence of transition matrices on a finite state space which converge to a limit transition matrix P. Let {Xn} be the associated non-homogeneous Markov chain where Pn controls movement from ti...

Large Deviations without Principle

We develop a methodology for studying “large deviations type” questions. Our approach does not require that the large deviations principle holds, and is thus applicable to a larg class of systems. We study a system of queues with exponential servers, which share an arrival stream. Arrivals are routed to the (weighted) shortest queue. It is not known whether the large deviations principle holds ...

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 ...