Homotopy probability theory II

Homotopy Probability Theory Ii

This is the second of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. This paper outlines how the framework can assist in the development of homotopy probability theory, where a vector space of random variables is replaced by a chain complex of random variables. This allows the principles of derived mathe...

Homotopy Probability Theory

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability theory, allowing the principles of deri...

Homotopy Probability Theory I

This is the first of two papers that introduce a deformation theoretic framework to explain and broaden a link between homotopy algebra and probability theory. In this paper, cumulants are proved to coincide with morphisms of homotopy algebras. The sequel paper outlines how the framework presented here can assist in the development of homotopy probability theory, allowing the principles of deri...

Cones in Homotopy Probability Theory

This note defines cones in homotopy probability theory and demonstrates that a cone over a space is a reasonable replacement for the space. The homotopy Gaussian distribution in one variable is revisited as a cone on the ordinary Gaussian.

Probability Theory II