A generalized white noise space approach to stochastic integration for a class of Gaussian stationary increment processes

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 asso...

Full description

Saved in:

Bibliographic Details
Published in:	Rocznik Akademii Górniczo-Hutniczej im. Stanisława Staszica. Opuscula Mathematica Vol. 33; no. 3; pp. 395 - 417
Main Authors:	Alpay, Daniel, Kipnis, Alon
Format:	Journal Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2013
Subjects:	fractional Brownian motion stochastic integral white noise space
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	1232-9274
DOI:	10.7494/OpMath.2013.33.3.395