Large Deviations for Occupation Measures for Markov Processes
نویسنده
چکیده
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 applications) on more natural one. It is given an example of Markov process, defined by non linear recursion, for which sufficient conditions of existing the large deviation principle are easy verified.
منابع مشابه
Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems
A classical damping Hamiltonian system perturbed by a random force is considered. The locally uniform large deviation principle of Donsker and Varadhan is established for its occupation empirical measures for large time, under the condition, roughly speaking, that the force driven by the potential grows in nitely at in nity. Under the weaker condition that this force remains greater than some p...
متن کاملAccelerated 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...
متن کاملLarge Deviations Asymptotics and the Spectral Theory of Multiplicatively Regular Markov Processes
In this paper we continue the investigation of the spectral theory and exponential asymptotics of primarily discrete-time Markov processes, following Kontoyiannis and Meyn [34]. We introduce a new family of nonlinear Lyapunov drift criteria, which characterize distinct subclasses of geometrically ergodic Markov processes in terms of simple inequalities for the nonlinear generator. We concentrat...
متن کاملFluctuations of Interacting Markov Chain Monte Carlo Methods
We present a multivariate central limit theorem for a general class of interacting Markov chain Monte Carlo algorithms used to solve nonlinear measure-valued equations. These algorithms generate stochastic processes which belong to the class of nonlinear Markov chains interacting with their empirical occupation measures. We develop an original theoretical analysis based on resolvent operators a...
متن کاملDenumerable Constrained Markov Decision Processes and Finite Approximations
The purpose of this paper is two fold. First to establish the Theory of discounted constrained Markov Decision Processes with a countable state and action spaces with general multi-chain structure. Second, to introduce nite approximation methods. We deene the occupation measures and obtain properties of the set of all achievable occupation measures under the diierent admissible policies. We est...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999