Equivalence of Probability Laws for a Class of Infinitely Divisible Random Measures

This is the extended exposition of the previous paper [2]. Given an infinitely divisible (or ID) random measure A on a measurable space T, we provide a certain method to construct a version of A based on a Poisson random measure on the product space S = T×(R＼{0}). In particular, the present paper contains a new result about a class of ID random measures on T which are realized by R-valued signed measures on T. As an application we discuss the law equivalence of ID random measures on T by using our constructive method with Kakutani's theorem on the equivalence of infinite product probability measures.Article信州大学理学部紀要 31(2): 71-80(1997)departmental bulletin pape