A method for designing asynchronous probabilistic processes

Abstract

25 pagesWe present a method for constructing asynchronous probabilistic processes. The asynchronous probabilistic processes thus obtained are called invariant. They generalize the familiar independent and identically distributed sequences of random variables to an asynchronous framework. Invariant processes are shown to be characterised by a finite family of real numbers, their characteristic numbers. Our method provides first a way to obtaining necessary and sufficient normalization conditions for a finite family of real numbers to be the characteristic numbers of some invariant asynchronous probabilistic process; and second, a procedure for constructing new asynchronous probabilistic processes