White noise based stochastic calculus associated with a class of Gaussian processes

Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spac...

Full description

Bibliographic Details
Main Authors:	Daniel Alpay, Haim Attia, David Levanony
Format:	Article
Language:	English
Published:	AGH Univeristy of Science and Technology Press 2012-01-01
Series:	Opuscula Mathematica
Subjects:	white noise space Wick product stochastic integral
Online Access:	http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3228.pdf

id	doaj-ad2c693a01f1484dab0256e06cfb93a8
record_format	Article
spelling	doaj-ad2c693a01f1484dab0256e06cfb93a82020-11-24T21:00:03ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742012-01-01323401422http://dx.doi.org/10.7494/OpMath.2012.32.3.4013228White noise based stochastic calculus associated with a class of Gaussian processesDaniel Alpay0Haim Attia1David Levanony2Ben Gurion University of the Negev, Department of Mathematics, P.O.B. 653, Be'er Sheva 84105, IsraelSami Shamoon College of Engineering, Department of Mathematics, Be'er Sheva 84100, IsraelBen Gurion University of the Negev, Department of Electrical Engineering, P.O.B. 653, Be'er Sheva 84105, IsraelUsing the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3228.pdfwhite noise spaceWick productstochastic integral
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Daniel Alpay Haim Attia David Levanony
spellingShingle	Daniel Alpay Haim Attia David Levanony White noise based stochastic calculus associated with a class of Gaussian processes Opuscula Mathematica white noise space Wick product stochastic integral
author_facet	Daniel Alpay Haim Attia David Levanony
author_sort	Daniel Alpay
title	White noise based stochastic calculus associated with a class of Gaussian processes
title_short	White noise based stochastic calculus associated with a class of Gaussian processes
title_full	White noise based stochastic calculus associated with a class of Gaussian processes
title_fullStr	White noise based stochastic calculus associated with a class of Gaussian processes
title_full_unstemmed	White noise based stochastic calculus associated with a class of Gaussian processes
title_sort	white noise based stochastic calculus associated with a class of gaussian processes
publisher	AGH Univeristy of Science and Technology Press
series	Opuscula Mathematica
issn	1232-9274
publishDate	2012-01-01
description	Using the white noise space setting, we define and study stochastic integrals with respect to a class of stationary increment Gaussian processes. We focus mainly on continuous functions with values in the Kondratiev space of stochastic distributions, where use is made of the topology of nuclear spaces. We also prove an associated Ito formula.
topic	white noise space Wick product stochastic integral
url	http://www.opuscula.agh.edu.pl/vol32/3/art/opuscula_math_3228.pdf
work_keys_str_mv	AT danielalpay whitenoisebasedstochasticcalculusassociatedwithaclassofgaussianprocesses AT haimattia whitenoisebasedstochasticcalculusassociatedwithaclassofgaussianprocesses AT davidlevanony whitenoisebasedstochasticcalculusassociatedwithaclassofgaussianprocesses
_version_	1716780514049785856

White noise based stochastic calculus associated with a class of Gaussian processes

Similar Items