White noise approach to Gaussian random fields

Ke-Seung Lee
1990 Nagoya mathematical journal  
The purpose of this paper is to investigate way of dependency of Gaussian random fieldsX(D)indexed by a domainDin d-dimensional Euclidean spaceRd. Our main tool is variational calculus, where the boundary of a domain varies and deforms and we appeal to the white noise analysis. We therefore assume thatX(D)is expressed white noise integral of the form(0.1)X(D)=X(D, W)=∫DF(D, u)W(u)du,whereWis theRd-parameter white noise and the kernelF(D, u)is a square integrable function overRd, and whereDis a
more » ... Rd, and whereDis a bounded domain with smooth boundary.
doi:10.1017/s0027763000003135 fatcat:n7sar6bnvvdrfjgvhcfiwdgxla