On Free Stochastic Processes and their Derivatives

Authors

Daniel Alpay, Chapman UniversityFollow
Palle Jorgensen, University of Iowa
Guy Salomon, Ben Gurion University of the Negev

Document Type

Article

Publication Date

2014

Abstract

We study a family of free stochastic processes whose covariance kernels K may be derived as a transform of a tempered measure σ. These processes arise, for example, in consideration non-commutative analysis involving free probability. Hence our use of semi-circle distributions, as opposed to Gaussians. In this setting we find an orthonormal bases in the corresponding noncommutative L2 of sample-space. We define a stochastic integral for our family of free processes.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Stochastic Processes and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stochastic Processes and Applications, volume 214, in 2014. DOI: 10.1016/j.spa.2014.05.007

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Recommended Citation

D. Alpay, P. Jorgensen and G. Salomon. On free stochastic processes and their derivatives. Stochastic Processes and their Applications, vo. 214 (2014), 3392-3411

Peer Reviewed

1

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.