Bernoulli

  • Bernoulli
  • Volume 13, Number 1 (2007), 252-278.

On layered stable processes

Christian Houdré and Reiichiro Kawai

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Abstract

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, over short intervals it is close to a stable process, while over long intervals it approximates another stable (possibly Gaussian) process. The absolute continuity of a layered stable process with respect to its short-range limiting stable process is also investigated. A series representation of layered stable processes is derived, giving insights into the structure both of the sample paths and of the short- and long-range behaviours of the process. This series representation is further used for simulation of sample paths.

Article information

Source
Bernoulli, Volume 13, Number 1 (2007), 252-278.

Dates
First available in Project Euclid: 30 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1175287732

Digital Object Identifier
doi:10.3150/07-BEJ5034

Mathematical Reviews number (MathSciNet)
MR2307406

Zentralblatt MATH identifier
1121.60052

Keywords
layered stable distributions and processes Lévy processes stable distributions and processes

Citation

Houdré, Christian; Kawai, Reiichiro. On layered stable processes. Bernoulli 13 (2007), no. 1, 252--278. doi:10.3150/07-BEJ5034. https://projecteuclid.org/euclid.bj/1175287732


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