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...
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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 |