Additive Functionals for Discrete-Time Markov Chains with Applications to Birth-Death Processes

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 ...

Two-Time-Scale Markov Chains and Applications to Quasi-Birth-Death Queues

Aiming at reduction of complexity, this work is concerned with two-time-scale Markov chains and applications to quasi-birth-death queues. Asymptotic expansions of probability vectors are constructed and justified. Lumping all states of the Markov chain in each subspace into a single state, an aggregated process is shown to converge to a continuous-time Markov chain whose generator is an average...

Transformations Of_ Markov Processes Connected with Additive Functionals

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...).

Linear functionals and Markov chains associated with Dirichlet processes

By investigating a Markov chain whose limiting distribution corresponds to that of the Dirichlet process we are able directly to ascertain conditions for the existence of linear functionals of that process. Together with earlier analyses we are able to characterize those functionals which are a.s. finite in terms of the parameter measure of the process. We also show that the appropriate Markov ...