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We prove a central limit theorem for linear triangular arrays under weak dependence conditions. Our result is then applied to the study of dependent random variables sampled by a Z-valued transient random walk. This extends the results obtained by Guillotin-Plantard & Schneider (2003). An application to parametric estimation by random sampling is also… (More)

We study the asymptotic behavior of the simple random walk on oriented versions of Z 2. The considered lattices are not directed on the vertical axis but unidirectional on the horizontal one, with random orientations whose distributions are generated by a dynamical system. We find a sufficient condition on the smoothness of the generation for the transience… (More)

- Frédérique Duheille-Bienven¨ue, Nadine Guillotin-Plantard

The purpose of the present paper is to study the asymptotic behaviour of the products of random matrices indexed by a random walk following the results obtained by Furstenberg and Kesten [4] and by Ishitani [6].

The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context in which such processes can arise. To our knowledge, discretisation and convergence theorems are available only in the… (More)

- Fabienne Castell, Nadine Guillotin-Plantard, Bruno Schapira
- 2013

Random walks in random scenery are processes defined by Zn := n k=1 ξX 1 +...+X k , where (X k , k ≥ 1) and (ξy, y ∈ Z) are two independent sequences of i.i.d. random variables. We assume here that their distributions belong to the normal domain of attraction of stable laws with index α ∈ (0, 2] and β ∈ (0, 2] respectively. These processes were first… (More)

We prove a non-standard functional limit theorem for a two dimensional simple random walk on some randomly oriented lattices. This random walk, already known to be transient, has different horizontal and vertical fluctuations leading to different normalizations in the functional limit theorem, with a non-Gaussian horizontal behavior. We also prove that the… (More)

Let S = (S k) k≥0 be a random walk on Z and ξ = (ξ i) i∈Z a stationary random sequence of centered random variables, independent of S. We consider a random walk in random scenery that is the sequence of random variables (Σ n) n≥0 where Σ n = n k=0 ξ S k , n ∈ N. Under a weak dependence assumption on the scenery ξ we prove a functional limit theorem… (More)

We consider a stochastic version of the k-server problem in which k servers move on a circle to satisfy stochastically generated requests. The requests are independent and identically distributed according to an arbitrary distribution on a circle, which is either discrete or continuous. The cost of serving a request is the distance that a server needs to… (More)

Random walks in random scenery are processes defined by Zn := n k=1 ωS k where S := (S k , k ≥ 0) is a random walk evolving in Z d and ω := (ωx, x ∈ Z d) is a sequence of i.i.d. real random variables. Under suitable assumptions on the random walk S and the random scenery ω, almost surely with respect to ω, the correctly renormalized sequence (Zn) n≥1 is… (More)