摘要
A generalized N-parameter Ornstein-Uhlenbeck process （GOUPN） is defined asX（t）=[f（t）]-1integral from n=a to t f（s）（ds）,t∈RaN, where a=（0…, 0） or （-∞, …, -∞）, correspondently RaN=R+Nor RN, and η（ds） is the standard Gaussian orthogonal random measure and f is an infinitely differentiable and locally quadratically integrable positive function. In this paper it is proved that the GOUPNhas the so called germ-Markov property with respect to any bounded domain, and two examples are given which say that for spherical and some pyramid-like domains, the minimal splitting σ-algebras for the 'interior' and the 'onter' information σ-algebras are strictly 'larger' than the boundary information σ-algebras.
A generalized N-parameter Ornstein-Uhlenbeck process （GOUP<sub>N</sub>） is defined asX（t）=[f（t）]<sup>-1</sup> integral from n=a to t f（s）（ds）,t∈R<sub>a</sub><sup>N</sup>, where a=（0…, 0） or （-∞, …, -∞）, correspondently R<sub>a</sub><sup>N</sup>=R<sub>+</sub><sup>N</sup> or R<sup>N</sup>, and η（ds） is the standard Gaussian orthogonal random measure and f is an infinitely differentiable and locally quadratically integrable positive function. In this paper it is proved that the GOUP<sub>N</sub> has the so called germ-Markov property with respect to any bounded domain, and two examples are given which say that for spherical and some pyramid-like domains, the minimal splitting σ-algebras for the 'interior' and the 'onter' information σ-algebras are strictly 'larger' than the boundary information σ-algebras.
