Random walks at random times: convergence to iterated Lévy motion, fractional stable motions, and other self-similar processes

DOI10.1214/12-AOP770zbMath1306.60038arXiv1105.3130OpenAlexW3100958930MaRDI QIDQ359684

Greg Markowsky, Paul H. Jung

Publication date: 22 August 2013

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.3130

zbMATH Keywords

random walksfractional Brownian motionself-similar processesiterated Lévy motionlocal times fractional stable motion

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Fractional processes, including fractional Brownian motion (60G22) Sums of independent random variables; random walks (60G50) Self-similar stochastic processes (60G18) Stable stochastic processes (60G52)

Related Items (1)

Random-time isotropic fractional stable fields

Cites Work

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• Discrete approximation of a stable self-similar stationary increments process
• Limit theorem for random walk in weakly dependent random scenery
• Indicator fractional stable motions
• The range of stable random walks
• Laws of the iterated logarithm for \(\alpha\)-time Brownian motion
• Random rewards, fractional Brownian local times and stable self-similar processes
• A functional approach for random walks in random sceneries
• Probabilistic construction of the solution of some higher order parabolic differential equation
• Occupation densities
• Weak convergence to fractional Brownian motion in Brownian scenery
• Stochastic calculus for Brownian motion on a Brownian fracture
• A law of the iterated logarithm for stable processes in random scenery
• Local times for a class of Markoff processes
• Null flows, positive flows and the structure of stationary symmetric stable processes
• Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions
• A limit theorem related to a new class of self similar processes
• α-time fractional Brownian motion: PDE connections and local times
• Random walk in random scenery: A survey of some recent results
• Probability

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