Identification of noncausal Ito processes from the stochastic Fourier coefficients II

We consider the identification problem of a noncausal Ito process from its stochastic Fourier coefficients with respect to the complete system of trigonometric functions. Here, a noncausal Ito process is the extension of Ito process whose diffusion and drift terms are assumed to be noncausal. If noncausal Ito processes are defined through Skorokhod integral, then authors obtained the affirmative answer in the previous article (Ogawa & Uemura,2014). In this note we generalize our result. We assume both diffusion and drift terms belong to the Watanabe space and identify the noncausal Ito process from its stochastic Fourier coefficients in the framework of Malliavin calculus.

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