Opuscula Math. 32, no. 3 (2012), 401-422
White noise based stochastic calculus associated with a class of Gaussian processes
Daniel Alpay
Haim Attia
David Levanony
Abstract.
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.
Keywords:
white noise space, Wick product, stochastic integral.
Mathematics Subject Classification:
60H40, 60H05, 60G15, 60G22, 46A12.
About the authors ▼
Daniel Alpay
Ben Gurion University of the Negev, Department of Mathematics, P.O.B. 653, Be'er Sheva 84105, Israel
Haim Attia
Sami Shamoon College of Engineering, Department of Mathematics, Be'er Sheva 84100, Israel
David Levanony
Ben Gurion University of the Negev, Department of Electrical Engineering, P.O.B. 653, Be'er Sheva 84105, Israel
About the article ▼
Received: 2011-11-30.
Revised: 2011-12-04.
Accepted: 2011-12-11.
Cite this article as ▼
Daniel Alpay, Haim Attia, David Levanony, White noise based stochastic calculus associated with a class of Gaussian processes, Opuscula Math. 32, no. 3 (2012), 401-422,
http://dx.doi.org/10.7494/OpMath.2012.32.3.401.
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