JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, v.10, no.3, pp.425 - 435
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.