CENTRAL LIMIT THEOREM FOR BIFURCATING MARKOV CHAINS UNDER L 2 -ERGODIC CONDITIONS

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

We define the kernel estimator and state the main results on the estimation of the density of µ, see Lemma 3.5 (consistency) and Theorem 3.6 (asymptotic normality), in Section 3.1.

The literature on approximations of diffusions with atoms in the speed measure is scarce. We remark that [1] provides a sequence of random walks that converges in distribution to

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

To check Conditions (A4) and (A4’) in Theorem 1, we need the next probabilistic results based on a recent version of the Berry-Esseen theorem derived by [HP10] in the

The goal of this paper is to show that the Keller-Liverani theorem also provides an interesting way to investigate both the questions (I) (II) in the context of geometrical

As an exception, let us mention the result of Adamczak, who proves in [Ada08] subgaussian concentration inequalities for geometrically ergodic Markov chains under the

The quantities g a (i, j), which appear in Theorem 1, involve both the state of the system at time n and the first return time to a fixed state a. We can further analyze them and get