Opuscula Math. 32, no. 3 (2012), 401-422
White noise based stochastic calculus associated with a class of Gaussian processes
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.
- Received: 2011-11-30.
- Revised: 2011-12-04.
- Accepted: 2011-12-11.