A Criterion for the Equivalence of two Stationary Gaussian Processes with, Not Necessarily Rational, Spectral Densities

概要

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The question concerning the equivalence of stationary Gaussian processes defined on the finite interval [0, T] was fully solved in the case where their spectral densities are rational in λ, (cf. [1], [5] and [7]). The object of this paper is to consider a criterion for the equivalence of two one-dimensional stationary Gaussian processes on [0, T] with, not necessarily rational, spectral densities (Theorem 2) : The main result is that P_ξ^T_<10> and P_ξ^T_<20> are equivalent if f_1(λ) and f_2(λ) are positive for almost all λ and if [numerical formula].
横浜国立大学の論文