Local limit theorem for densities of the additive component of a finite Markov Additive Process

Central and Local Limit Theories in Markov Dependent Random Variables

Limit theorems for stationary Markov processes with L2-spectral gap

Let (Xt, Yt)t∈T be a discrete or continuous-time Markov process with state space X × R where X is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. (Xt, Yt)t∈T is assumed to be a Markov additive process. In particular, this implies that the first component (Xt)t∈T is also a Markov process. Markov random walks or additive f...

Central and Local Limit Theorems in Markov Dependent Random Variables

We consider an irreducible and aperiodic Markov chain {kn}n=0 over the finite state space E = {1, . . . , p} with positive regular transition matrix P = {pij} and additive component {Un} such that {Sn} = {(kn, Un)} is also a Markov chain over the state space E1 = E × R. We prove a central and a local limit theorem for this chain when the probability density functions of {Sn}, conditional on the...

Additional material on local limit theorem for finite Additive Markov Processes [HL13]

This paper proposes additional material to the main statements of [HL13] which are are recalled in Section 2. In particular an application of [HL13, Th 2.2] to Renewal Markov Processes is provided in Section 4 and a detailed checking of the assumptions of [HL13, Th 2.2] for the joint distribution of local times of a finite jump process is reported in Section 5. A uniform version of [HL13, Th 2....

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 ...