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.
- 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
- Received: 2011-11-30.
- Revised: 2011-12-04.
- Accepted: 2011-12-11.
