Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1157133 | Stochastic Processes and their Applications | 2006 | 16 Pages |
Abstract
We study a non-Gaussian and non-stable process arising as the limit of sums of rescaled renewal processes under the condition of intermediate growth. The process has been characterized earlier by the cumulant generating function of its finite-dimensional distributions. Here, we derive a more tractable representation for it as a stochastic integral of a deterministic function with respect to a compensated Poisson random measure. Employing the representation we show that the process is locally and globally asymptotically self-similar with fractional Brownian motion and stable Lévy motion as its tangent limits.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Raimundas Gaigalas,