Displaying similar documents to “A characterization and moving average representation for stable harmonizable processes.”

Disjointness results for some classes of stable processes

Michael Hernández, Christian Houdré (1993)

Studia Mathematica

Similarity:

We discuss the disjointness of two classes of stable stochastic processes: moving averages and Fourier transforms. Results on the incompatibility of these two representations date back to Urbanik. Here we extend various disjointness results to encompass larger classes of processes.

Long memory and self-similar processes

Gennady Samorodnitsky (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

This paper is a survey of both classical and new results and ideas on long memory, scaling and self-similarity, both in the light-tailed and heavy-tailed cases.

On measure-preserving transformations and doubly stationary symmetric stable processes

A. Gross, A. Weron (1995)

Studia Mathematica

Similarity:

In a 1987 paper, Cambanis, Hardin and Weron defined doubly stationary stable processes as those stable processes which have a spectral representation which is itself stationary, and they gave an example of a stationary symmetric stable process which they claimed was not doubly stationary. Here we show that their process actually had a moving average representation, and hence was doubly stationary. We also characterize doubly stationary processes in terms of measure-preserving regular...

Generalized tempered stable processes

Jan Rosiński, Jennifer L. Sinclair (2010)

Banach Center Publications

Similarity:

This work introduces the class of generalized tempered stable processes which encompass variations on tempered stable processes that have been introduced in the field, including "modified tempered stable processes", "layered stable processes", and "Lamperti stable processes". Short and long time behavior of GTS Lévy processes is characterized and the absolute continuity of GTS processes with respect to the underlying stable processes is established. Series representations of GTS Lévy...

Approximation of finite-dimensional distributions for integrals driven by α-stable Lévy motion

Aleksander Janicki (1999)

Applicationes Mathematicae

Similarity:

We present a method of numerical approximation for stochastic integrals involving α-stable Lévy motion as an integrator. Constructions of approximate sums are based on the Poissonian series representation of such random measures. The main result gives an estimate of the rate of convergence of finite-dimensional distributions of finite sums approximating such stochastic integrals. Stochastic integrals driven by such measures are of interest in constructions of models for various problems...