Long time asymptotics of unbounded additive functionals of Markov processes

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...

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...).

Transformations Of_ Markov Processes Connected with Additive Functionals

Additive Functionals for Discrete-time Markov Chains with Applications to Birth–death Processes

In this paper we are interested in bounding or calculating the additive functionals of the first return time on a set for discrete-time Markov chains on a countable state space, which is motivated by investigating ergodic theory and central limit theorems. To do so, we introduce the theory of the minimal nonnegative solution. This theory combined with some other techniques is proved useful for ...

Additive functionals and excursions of Kuznetsov processes

Let B be a continuous additive functional for a standard process (Xt)t∈R+ and let (Yt)t∈R be a stationary Kuznetsov process with the same semigroup of transition. In this paper, we give the excursion laws of (Xt)t∈R+ conditioned on the strict past and future without duality hypothesis. We study excursions of a general regenerative system and of a regenerative system consisting of the closure of...