Representation of gaussian processes equivalent to a gaussian martingalet

Abstract

This paper states that a Gaussian process Y with mean 0 is equivalent to a Gaussian martingale starting from 0 if and only if Y is a semi-martingale with Gaussian martingale part and Gaussian “clrift” of a particular kind. We also obtain a theorem of Girsanov type tor Gaussian martingales and a criterion for the equivalence mentioned above in more convenient terms. Our results extend those of M. Hitsuda [8] concerning equivalence to a Wiener process

^†This Paper is dedicated to professor A.N. Shriyaev on the occassion of his 45th birthday It was presented at the 12th European Meeting of Statisticians, Varna, Bulgaria, September 3-7, 1979

^†This Paper is dedicated to professor A.N. Shriyaev on the occassion of his 45th birthday It was presented at the 12th European Meeting of Statisticians, Varna, Bulgaria, September 3-7, 1979

Notes

^†This Paper is dedicated to professor A.N. Shriyaev on the occassion of his 45th birthday It was presented at the 12th European Meeting of Statisticians, Varna, Bulgaria, September 3-7, 1979