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White noise based stochastic calculus associated with a class of Gaussian processes

Alpay D., Attia H., Levanony D.

Opuscula Mathematica

2012

Vol. 32, no. 3

401-422

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.