Random measure algebras

Author:

Park Jason

Abstract

In this article, we introduce algebras of random measures. Algebra is a vector space V V over a field F F with a multiplication satisfying the property: 1) distribution and 2) c ( x y ) = ( c x ) y = x ( c y ) c(x\cdot y) = (cx)\cdot y = x\cdot (cy) for every c F c \in F and x , y V x, y \in V . The first operation is a trivial addition operation. For the second operation, we present three different methods 1) a convolution by covariance method, 2) O-dot product, 3) a convolution of bimeasures by Morse-Transue integral. With those operations, it is possible to build three different algebras of random measures.

Publisher

American Mathematical Society

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