A Generalized White Noise Space Approach To Stochastic Integration for a Class of Gaussian Stationary Increment Processes

Authors

Daniel Alpay, Chapman UniversityFollow
Alon Kipnis, Ben Gurion University of the Negev

Document Type

Article

Publication Date

2013

Abstract

Given a Gaussian stationary increment processes, we show that a Skorokhod-Hitsuda stochastic integral with respect to this process, which obeys the Wick-Itô calculus rules, can be naturally defined using ideas taken from Hida’s white noise space theory. We use the Bochner-Minlos theorem to associate a probability space to the process, and define the counterpart of the S-transform in this space. We then use this transform to define the stochastic integral and prove an associated Itô formula.

Comments

This article was originally published in Opuscula Mathematica, volume 33, issue 3, in 2013 DOI: 10.7494/OpMath.2013.33.3.395

Recommended Citation

D. Alpay and A. Kipnis. A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes. Opuscula Mathematica, vol. 33 (2013), pp. 395-417.

Peer Reviewed

1

Copyright

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