Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains

For branching random walks (possibly in varying environment in time and space), the auxiliary Markov chain Y is a random walk (possibly in varying environment in time and space)..

Consequently, if ξ is bounded, the standard perturbation theory applies to P z and the general statements in Hennion and Herv´e (2001) provide Theorems I-II and the large

Additive functionals, Markov chains, Renewal processes, Partial sums, Harris recurrent, Strong mixing, Absolute regularity, Geometric ergodicity, Invariance principle,

We point out that the regenerative method is by no means the sole technique for obtain- ing probability inequalities in the markovian setting.. Such non asymptotic results may

chains., Ann. Nagaev, Some limit theorems for stationary Markov chains, Teor. Veretennikov, On the Poisson equation and diffusion approximation. Rebolledo, Central limit theorem

In this section, we exhibit several examples of Markov chains satisfying H (p) (for different norms) for which one can prove a lower bound for the deviation probability of

Recently, potential theory and the Dirichlet principle played an important role in the proof of almost sure convergence of Dirichlet functions in transient Markov processes [1, 6],

It is possible to develop an L 2 (µ) approach result similar to Corollary 3.4. Preliminary results for the kernel estimation.. Statistical applications: kernel estimation for