Equivalence of measures for some class of Gaussian random fields

K. Inoue

Journal of Multivariate Analysis, 1976, vol. 6, issue 2, 295-308

Abstract: We consider two Gaussian measures P1 and P2 on (C(G), ) with zero expectations and covariance functions R1(x, y) and R2(x, y) respectively, where R[nu](x, y) is the Green's function of the Dirichlet problem for some uniformly strongly elliptic differential operator A([nu]) of order 2m, m >= [d/2] + 1, on a bounded domain G in d ([nu] = 1, 2). It is shown that if the order of A(2) - A(1) is at most 2m - [d/2] - 1, then P1 and P2 are equivalent, while if the order is greater than 2m - [d/2] - 1, then P1 and P2 are not always equivalent.

Keywords: Equivalence; of; Gaussian; measures; Green's; function; of; the; Dirichlet; problem (search for similar items in EconPapers)
Date: 1976
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