Loïc Hervé

Limit theorems for stationary Markov processes with L2-spectral gap

Let

Spectral analysis of Markov kernels and application to the convergence rate of discrete random walks

(X_t, Y_t)_{t\in \mathbb{T}}

Computable bounds of

be a discrete or continuous-time Markov process with state space

{\ell}^2

\mathbb{X} \times \mathbb{R}^d

-spectral gap for discrete Markov chains with band transition matrices

where

The Nagaev-Guivarc'h method via the Keller-Liverani theorem

\mathbb{X}

Regular perturbation of V-geometrically ergodic Markov chains

is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e.

Quasi-compactness of Markov kernels on weighted-supremum spaces and geometrical ergodicity

(X_t, Y_t)_{t\in \mathbb{T}}

On the Recurrence Set of Planar Markov Random Walks

is assumed to be a Markov additive process. In particular, this implies that the first component

The Nagaev method via the Keller-Liverani theorem

(X_t)_{t\in \mathbb{T}}