This article deals with the asymptotic behavior as t →+ ∞ of the survival function PT> t,
where T is the first passage time above a non negative level of a random process starting …

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

Persistence of iterated partial sums Page 1 www.imstat.org/aihp Annales de l’Institut Henri
Poincaré - Probabilités et Statistiques 2013, Vol. 49, No. 3, 873–884 DOI: 10.1214/11-AIHP452 …

For a class of one-dimensional autoregressive sequences (X_n)(X n), we consider the tail
behaviour of the stop** time T_0=\min { n ≥ 1: X_n ≤ 0 } T 0= min n≥ 1: X n≤ 0. We …

Some general theoretical works on Gaussian measures are also included whenever they
treat inequalities widely used in small deviation theory. Also included are the relevant …

Given an autoregressive process X of order p (ie Xn= a1Xn− 1+···+ apXn− p+ Yn where the
random variables Y1, Y2,... are iid), we study the asymptotic behaviour of the probability that …

We prove that an integrated simple random walk, where random walk and integrated
random walk are conditioned to return to zero, has asymptotic probability n− 1/2 to stay …

We prove the existence of the persistence exponent log λ:= lim n→∞ 1 n log P μ (X 0∈ S,…,
X n∈ S) for a class of time homogeneous Markov chains {X i} i≥ 0 taking values in a Polish …

With {ξ i} i≥ 0 being a centered stationary Gaussian sequence with non-negative correlation
function ρ (i)≔ E [ξ 0 ξ i] and {σ (i)} i≥ 1 a sequence of positive reals, we study the …

This work establishes exact formulae for the persistence probabilities pk (θ)= P [Y 1⩾ 0,…, Y
k⩾ 0] of an AR (1) sequence Y n= θ Y n− 1+ X n, n= 1, 2,… with parameter θ∈ R﹨(1 2, 2) …