deviation bounds for additive functionals of 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...

Transformations Of_ Markov Processes Connected with Additive Functionals

Large Deviation Bounds for Markov Chains

We study the fraction of time that a Markov chain spends in a given subset of states. We give an exponential bound on the probability that it exceeds its expectation by a constant factor. Our bound depends on the mixing properties of the chain, and is asymptotically optimal for a certain class of Markov chains. It beats the best previously known results in this direction. We present an applicat...

Small Deviation Estimates for Some Additive Processes

We study the small deviation probabilities for real valued additive processes. This naturally leads to the small deviation for the corresponding range process. Our general results can be applied to a wide range of additive processes generated from fractional Brownian motions, stable processes, Brownian sheets, etc. As an application, limit inf type LIL are proved for additive stable processes.