Seminar Peter Carr Seminar

Abstract

In pseudo-calculus, pseudo-sum and a pseudo-product substitute and generalize the usual sum and multiplication: by the same way of reasoning, the standard notion of probability is generalized by a distorted probability called "pseudo-probability".

In this framework, we introduce a generalization of the notion of independence and of the moment generating function (both for random variables as well as for random vectors) with respect to a pseudo-probability and we show how classical results about moment-generating functions of a vector of independent random variables and of their sum extend to pesudo-moment generating functions if the random variables involved are pseudo-independent.

As an extension of the notion of Schur-constant bivariate random vectors in the usual probability space, we introduce a more general class of vectors using a non-commutative version of the pseudo-sum and we prove that the pseudo-calculus framework as well as the introduced concepts of pseudo-moment generating functions allow to extend some well-known characterizations of Schur-constant random vectors to the new more general class.