The Annals of Applied Probability

Random rewards, fractional Brownian local times and stable self-similar processes

Serge Cohen and Gennady Samorodnitsky

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Abstract

We describe a new class of self-similar symmetric α-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting models are different from the ones studied earlier both in their memory properties and smoothness of the sample paths.

Article information

Source
Ann. Appl. Probab., Volume 16, Number 3 (2006), 1432-1461.

Dates
First available in Project Euclid: 2 October 2006

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1159804987

Digital Object Identifier
doi:10.1214/105051606000000277

Mathematical Reviews number (MathSciNet)
MR2260069

Zentralblatt MATH identifier
1133.60016

Subjects
Primary: 60G18: Self-similar processes
Secondary: 60G52: Stable processes 60G17: Sample path properties

Keywords
Stable process self-similar process stationary process integral representation conservative flow null flow fractional Brownian motion local time random reward chaos expansion superposition of scaled inputs long memory

Citation

Cohen, Serge; Samorodnitsky, Gennady. Random rewards, fractional Brownian local times and stable self-similar processes. Ann. Appl. Probab. 16 (2006), no. 3, 1432--1461. doi:10.1214/105051606000000277. https://projecteuclid.org/euclid.aoap/1159804987


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