Application of Hilbert-Space Methods to Random Field Modelling and Estimation

SYNOPTIC ABSTRACT

In this paper we apply the theory of reproducing kernel Hilbert spaces (RKHS's) in relation to fractional Sobolev spaces to formulate and solve the problems of differential representation, orthogonal approximation and linear (direct and inverse) estimation of a class of fractional second-order random fields.

Key Words and Phrases:

• fractional random fields
• fractal sets
• least-squares linear estimation
• orthogonal expansions
• wavelets
• weak-sense Markov property
• Wiener-Hopf equation