Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 3, 328--336

A NOTE ON FUNCTIONALS OF A NON-GAUSSIAN DENSITY PROCESS VIA A NON-POISSON SYSTEM OF INDEPENDENT BROWNIAN MOTIONS

By

SRIKANTH K. IYER, Indian Institute of Technology, Kanpur

SUMMARY. A non-Gaussian density process was constructed in Feldman and Iyer (1998) as a limit of a functional over a non-Poisson system of infinitely many independent Brownian motions. We show that certain functionals (multiple integrals) of the limiting process can be obtained as weak limits of functionals over the particle system in the appropriate Skorohod space.

AMS (1991) subject classification. 60G60, 60F17; secondary. 60F05, 60E07.

Key words and phrases. Variance components, existence, maximum likelihood.

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