Large deviation for additive functionals of symmetric Markov processes

Deviation Bounds for Additive Functionals of Markov Processes

where X is a μ stationary and ergodic Markov process and V is some μ integrable function. These bounds are obtained under various moments assumptions for V , and various regularity assumptions for μ. Regularity means here that μ may satisfy various functional inequalities (F-Sobolev, generalized Poincaré etc...).

Non-markovian Limits of Additive Functionals of Markov Processes

Abstract. In this paper we consider an additive functional of an observable V (x) of a Markov jump process. We assume that the law of the expected jump time t(x) under the invariant probability measure π of the skeleton chain belongs to the domain of attraction of a subordinator. Then, the scaled limit of the functional is a Mittag-Leffler proces, provided that Ψ(x) := V (x)t(x) is square integ...

On Semi-martingale Characterizations of Functionals of Symmetric Markov Processes

Abstract For a quasi-regular (symmetric) Dirichlet space (E ,F) and an associated symmetric standard process (Xt, Px), we show that, for u ∈ F , the additive functional u∗(Xt) − u∗(X0) is a semimartingale if and only if there exists an E-nest {Fn} and positive constants Cn such that |E(u, v)| ≤ Cn‖v‖∞, v ∈ FFn,b. In particular, a signed measure resulting from the inequality will be automaticall...

Transformations Of_ Markov Processes Connected with Additive Functionals

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...