Dynamical attraction to stable processes

DOI10.1214/10-AIHP411zbMath1246.37020OpenAlexW2070973684MaRDI QIDQ424711

Marina Talet, Albert Meads Fisher

Publication date: 4 June 2012

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

Full work available at URL: https://projecteuclid.org/euclid.aihp/1334148210

zbMATH Keywords

Brownian motionstable processgeneric pointalmost-sure invariance principle in log densitypathwise central limit theoremscaling flow

Mathematics Subject Classification ID

Dynamical systems and their relations with probability theory and stochastic processes (37A50) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52) Functional limit theorems; invariance principles (60F17)

Related Items

Asymptotic self-similarity and order-two ergodic theorems for renewal flows

Cites Work

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• A note on the almost sure central limit theorem
• The self-similar dynamics of renewal processes
• Some limit theorems in log density
• Convex-invariant means and a pathwise central limit theorem
• A complete metric in the space \(D[0,\infty)\)
• Structure and continuity of measurable flows
• Almost sure functional limit theromes. Part II. The case of indepent random variables
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Some Useful Functions for Functional Limit Theorems
• An approximation of partial sums of independent RV's, and the sample DF. II
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• The approximation of partial sums of independent RV's
• Approximation of partial sums of i.i.d.r.v.s when the summands have only two moments
• On the tail behavior of sums of independent random variables
• A Comedy of Errors: The Canonical Form for a Stable Characteristic Function
• An invariance principle for the law of the iterated logarithm
• Weak Convergence of Stochastic Processes Defined on Semi-Infinite Time Intervals