Homotopy probability theory I

Abstract

This is the first of two papers that introduce a deformation theoretic frame work to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide withmorphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the develop ment of homotopy probability theory, allowing the principles of derived mathematics to participate in classical and noncommutative probability theory.