On Layered Stable Processes

Details On Layered Stable Processes On Layered Stable Processes

2005-03-31

arxiv.org/abs/math/0503742v1

Mathematics

Probability

22 pages, 9 figures

Scientific paper

Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a stable process while, in long time, it approximates another stable (possibly Gaussian) process. We also investigate the absolute continuity of a layered stable process with respect to its short time limiting stable process. A series representation of layered stable processes is derived, giving insights into both the structure of the sample paths and of the short and long time behaviors. This series is further used for sample paths simulation.

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