We consider random walks with independent but not necessarily identical distributed
increments. Assuming that the increments satisfy the well-known Lindeberg condition, we …

We study the asymptotic behaviour of the probability of non-extinction of a critical multi-type
Galton–Watson process in iid random environments by using limit theorems for products of …

Abstract Let (X_n) _ n\geqslant 0 (X n) n⩾ 0 be a Markov chain with values in a finite state
space XX starting at X_0= x ∈ XX 0= x∈ X and let f be a real function defined on X X. Set …

Consider a Markov chain (Xn) n≥ 0 with values in the state space 𝕏. Let f be a real function
on 𝕏 and set S n= Σ i= 1 nf X i, n≥ 1. Let ℙ x be the probability measure generated by the …

For a random walk killed at leaving a cone we suggest two new constructions of a positive
harmonic function. These constructions allow one to remove a quite strong extendability …

Our objective is to explore random walks on the general linear group, constrained to a
specific domain, with a primary focus on establishing the conditioned local limit theorem …

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In this paper we continue our study of a multidimensional random walk with zero mean and
finite variance killed on leaving a cone. We suggest a new approach that allows one to …

Inspired by a recent paper of I. Grama, E. Le Page and M. Peign\'e, we consider a sequence
$(g_n) _ {n\geq 1} $ of iid random $ d\times d $-matrices with non-negative entries and study …

Consider (gn) n≥ 1 a sequence of independent and identically distributed random matrices
and the left random walk G n:= gn… g 1, n≥ 1 on the general linear group GL (d, R). Under …