Opuscula Math. 32, no. 3 (2012), 401-422
http://dx.doi.org/10.7494/OpMath.2012.32.3.401

 
Opuscula Mathematica

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.

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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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