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

Abstract

We describe a new class of self-similar symmetric $\alpha$-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.

Published at http://dx.doi.org/10.1214/105051606000000277 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Extreme value theory, ergodic theory and the boundary between short memory and long memory for stationary stable processes

Cited by in corpus (4)

• Functional central limit theorem for heavy tailed stationary infinitely divisible processes generated by conservative flows
• Ergodic properties of sum- and max-stable stationary random fields via null and positive group actions
• Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses
• Random walks at random times: Convergence to iterated Lévy motion, fractional stable motions, and other self-similar processes