Scaling limits of Gaussian vector fields

Loren D. Pitt

Journal of Multivariate Analysis, 1978, vol. 8, issue 1, 45-54

Abstract: For Gaussian vector fields {X(t) [set membership, variant] Rn:t [set membership, variant] Rd} we describe the covariance functions of all scaling limits Y(t) = lim[alpha][downwards arrow]0 B-1([alpha]) X([alpha]t) which can occur when B([alpha]) is a d - d matrix function with B([alpha]) --> 0. These matrix covariance functions r(t, s) = EY(t) Y*(s) are found to be homogeneous in the sense that for some matrix L and each [alpha] > 0, (*) r([alpha]t, [alpha]s) = [alpha]L*r(t, s) [alpha]L. Processes with stationary increments satisfying (*) are further analysed and are found to be natural generalizations of Lévy's multiparameter Brownian motion.

Keywords: Scale; invariant; Gaussian; fields (search for similar items in EconPapers)
Date: 1978
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Citations: View citations in EconPapers (1)

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