61 citations · 155 across the 24 of their papers we have counts for
7 papers · 1 filter
Empirical processes for recurrent and transient random walks in random scenery
Nadine Guillotin-Plantard, Francoise Pene, Martin Wendler
In this paper, we are interested in the asymptotic behaviour of the sequence of processes with \begin{equation*} W_n(s,t):=\sum_{k=1}^{\lfloor nt\rfloor}…
The Sequential Empirical Process of a Random Walk in Random Scenery
Martin Wendler
A random walk in random scenery is given by for a random walk and iid random variables . In…
Two-Sample U-Statistic Processes for Long-Range Dependent Data
Herold Dehling, Aeneas Rooch, Martin Wendler
Motivated by some common-change point tests, we investigate the asymptotic distribution of the U-statistic process , $0\leq t\…
Convergence of U-statistics indexed by a random walk to stochastic integrals of a Levy sheet
Brice Franke, Francoise Pene, Martin Wendler
We establish limit theorems for U-statistics indexed by a random walk on Z^d and we express the limit in terms of some Levy sheet Z(s,t). Under some hypotheses, we prove that the l…
Stable Limit Theorem for U-Statistic Processes Indexed by a Random Walk
Brice Franke, Francoise Pene, Martin Wendler
Let (S_n)_{n\in\N} be a Z-valued random walk with increments from the domain of attraction of some α-stable law and let (ξ(i))_{i\in\Z} be a sequence of iid random variables. We wa…
Law of the Iterated Logarithm for U-Statistics of Weakly Dependent Observations
Herold Dehling, Martin Wendler
The law of the iterated logarithm for partial sums of weakly dependent processes was intensively studied by Walter Philipp in the late 1960s and 1970s. In this paper, we aim to ext…
Central Limit Theorem and the Bootstrap for U-Statistics of Strongly Mixing Data
Herold Dehling, Martin Wendler
The asymptotic normality of U-statistics has so far been proved for iid data and under various mixing conditions such as absolute regularity, but not for strong mixing. We use a co…