Limit theorems for one and two-dimensional random walks in random scenery

DOI10.1214/11-AIHP466zbMath1278.60046arXiv1103.4453MaRDI QIDQ1951508

Nadine Guillotin-Plantard, Françoise Pène, Fabienne Castell

Publication date: 6 June 2013

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.4453

zbMATH Keywords

local timelocal limit theoremstable processrandom walk in random scenery

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Processes in random environments (60K37) Stable stochastic processes (60G52)

Related Items (9)

Local limit theorem for randomly deforming billiards ⋮ Empirical processes for recurrent and transient random walks in random scenery ⋮ Chover-type laws of the iterated logarithm for Kesten-Spitzer random walks in random sceneries belonging to the domain of stable attraction ⋮ Central limit theorems for nearly long range dependent subordinated linear processes ⋮ Optimal bounds for the variance of self-intersection local times ⋮ Persistence probabilities for stationary increment processes ⋮ Exponential moments of self-intersection local times of stable random walks in subcritical dimensions ⋮ Limit theorems for additive functionals of random walks in random scenery ⋮ Quenched tail estimate for the random walk in random scenery and in random layered conductance. II.

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence of partial sum processes to Lévy processes for associated sequences
• Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory
• A local limit theorem for random walks in random scenery and on randomly oriented lattices
• The range of stable random walks
• Moderate and small deviations for the ranges of one-dimensional random walks
• Moments and distribution of the local time of a two-dimensional random walk
• Diffusion in layered random flows, polymers, electrons in random potentials, and spin depolarization in random fields
• A central limit theorem for two-dimensional random walks in random sceneries
• Scaling limit for trap models on \(\mathbb Z^d\)
• Stochastic-Process Limits
• A limit theorem related to a new class of self similar processes
• On the dynamics of trap models in ℤ ^d
• Limit theorems for Markov chains and stochastic properties of dynamical systems by quasi-compactness

This page was built for publication: Limit theorems for one and two-dimensional random walks in random scenery