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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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

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

First available in Project Euclid: 2 October 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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