Emile Le Page

A local limit theorem on the semi-direct product of ø*+ and ød

Abstract Let G be the semi-direct product of o*+ and od and μ, a probability measure on G. Let μ*n be the nth power of convolution of μ. Under quite general assumptions on μ, one proves that there exists ρ e [0, 1] such that the sequence of Radon measures (n3/2/ρn μ*n)n≥1 converges weakly to a non-degenerate measure; furthermore, if μk2/*n is the marginal of μ*n on od, the sequence of Radon measures (√n/ρn)n≥1 converges weakly to a non-degenerate measure.

Local limit theorems on some non unimodular groups

Let Gd be the semi-direct product of R*+ and Rd, d = 1 and let us consider the product group Gd,N = Gd x RN, N = 1. For a large class of probability measures µ on Gd,N, one prove that there exists ?(µ) I ]0,1] such that the sequence of finite measures {(n(N+3)/2 / ?(µ)n) µ*n}n = 1 converges weakly to a non-degenerate measure.

Limit theorems for affine Markov walks conditioned to stay positive

Consider the real Markov walk

Stable laws and spectral gap properties for affine random walks

S_n = X_1+ \dots+ X_n

LIMIT THEOREMS FOR MARKOV WALKS CONDITIONED TO STAY POSITIVE UNDER A SPECTRAL GAP ASSUMPTION

with increments

Homogeneity at Infinity of Stationary Solutions of Multivariate Affine Stochastic Recursions

\left(X_n\right)_{n\geq 1}

BOUNDS IN THE LOCAL LIMIT THEOREM FOR A RANDOM WALK CONDITIONED TO STAY POSITIVE

defined by a stochastic recursion starting at

On the multidimensional stochastic equation Yn+1 = AnYn + Bn

X_0=x

Régularité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes et applications

. For a starting point

Spectral gap properties and asymptotics of stationary measures for affine random walks

y>0