Empirical processes for recurrent and transient random walks in random scenery

DOI10.1051/ps/2019030zbMath1447.60073arXiv1711.10202OpenAlexW3009820678MaRDI QIDQ5110213

Françoise Pène, Martin Wendler, Nadine Guillotin-Plantard

Publication date: 18 May 2020

Published in: ESAIM: Probability and Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.10202

zbMATH Keywords

empirical processrandom walkrandom scenery

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Sums of independent random variables; random walks (60G50) Functional limit theorems; invariance principles (60F17)

Related Items

Chover-type laws of the iterated logarithm for Kesten-Spitzer random walks in random sceneries belonging to the domain of stable attraction ⋮ Limit theorems for additive functionals of random walks in random scenery

Cites Work

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• The quenched limiting distributions of a charged-polymer model
• Stable limit theorem for \(U\)-statistic processes indexed by a random walk
• Limit theorem for random walk in weakly dependent random scenery
• Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory
• The sequential empirical process of a random walk in random scenery
• Moments and distribution of the local time of a two-dimensional random walk
• Annealed deviations of random walk in random scenery
• The empirical process of some long-range dependent sequences with an application to U-statistics
• Nonparametric change-point estimation
• Moderate deviations for diffusions in a random Gaussian shear flow drift
• An embedding for the Kesten-Spitzer random walk in random scenery
• A law of the iterated logarithm for stable processes in random scenery
• A central limit theorem for two-dimensional random walks in random sceneries
• Annealed large deviations for diffusions in a random Gaussian shear flow drift.
• The change-point problem for dependent observations
• Quenched central limit theorems for random walks in random scenery
• Limit theorems for one and two-dimensional random walks in random scenery
• Random walk in random scenery and self-intersection local times in dimensions \(d \geq 5\)
• Change-point tests under local alternatives for long-range dependent processes
• Functional limit theorems for \(U\)-statistics indexed by a random walk.
• Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions
• TESTING FOR DISTRIBUTIONAL CHANGE IN TIME SERIES
• Central limit theorem for sampled sums of dependent random variables
• Strong invariance for local times
• An almost sure invariance principle for the empirical distribution function of mixing random variables
• A limit theorem related to a new class of self similar processes
• Limit theorems for U-statistics indexed by a one dimensional random walk
• Weak convergence of the empirical process of intermittent maps in 𝕃² under long-range dependence
• Random walk in random scenery: A survey of some recent results
• An intrinsic time for non-stationary finite markov chains
• Convergence Criteria for Multiparameter Stochastic Processes and Some Applications
• Skorohod embedding of multivariate RV's, and the sample DF

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