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

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

2006-10-09

arxiv.org/abs/math/0610272v1

Annals of Applied Probability 2006, Vol. 16, No. 3, 1432-1461

Mathematics

Probability

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

Scientific paper

10.1214/105051606000000277

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.

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