Asymptotic variance of the self-intersections of stable random walks using Darboux-Wiener theory

DOI10.1134/S0037446611040082zbMath1227.60059OpenAlexW2114093931MaRDI QIDQ642079

S. A. Utev, George Deligiannidis

Publication date: 25 October 2011

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0037446611040082

zbMATH Keywords

random walkself-intersectionDarboux-Wiener theory

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Processes in random environments (60K37) Functional limit theorems; invariance principles (60F17)

Related Items (9)

Local limit theorem for randomly deforming billiards ⋮ On the quenched functional CLT in random sceneries ⋮ Empirical processes for recurrent and transient random walks in random scenery ⋮ Limit theorems for one and two-dimensional 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 ⋮ Self-intersections of trajectories of the Lorentz process ⋮ Optimal bounds for the variance of self-intersection local times ⋮ CLT for random walks of commuting endomorphisms on compact abelian groups ⋮ Limit theorems for additive functionals of random walks in random scenery

Cites Work

• Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks
• Moments and distribution of the local time of a two-dimensional random walk
• A short proof of Darboux's lemma
• An invariance principle for certain dependent sequences
• Moment and probability bounds with quasi-superadditive structure for the maximum partial sum
• A law of the iterated logarithm for random walk in random scenery with deterministic normalizers
• A central limit theorem for two-dimensional random walks in random sceneries
• Central limit theorem for sampled sums of dependent random variables
• Singularity Analysis of Generating Functions
• A limit theorem related to a new class of self similar processes
• Tauberian theorems
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