论文信息 - Representation of Gaussian processes equivalent to Wiener process

Representation of Gaussian processes equivalent to Wiener process

The purpose of this paper is to get a canonical representation of Gaussian processes which are equivalent (or mutually absolutely continuous) to Wiener process. The main result is this. Suppose we are given a Gaussian process Yt on a probability space (Ω, 33, P), which is equivalent to Wiener process. Then a Wiener process Xt is constructed on (Ω, 33, P) as a functional of [Ys\ s^t] and, conversely, Yt is represented as a measurable functional of [Xs\ s^t} for each *<Ξ[0, T]. In case of £(Fί)=0, fe[0, Γ], Yt is represented by the formula

M. Hitsuda

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