Investigation of deformed stochastic bases of the 2nd kind

Deformations (special two-parameter families of probability measures) {Q(n,k), 0<=k<= n< .} and the corresponding deformed stochastic bases of the 1st and 2nd kind with discrete time were axiomatically determined by the first author in 2008. Subsequently, he and O.V. Nazarko laid the foundations of a stochastic analysis on these structures. The present work continues this topic. The main result of the paper is the theorem, which proves the formula for representing measures {Q(n,k), 0<=k< n< .} by the measures {Q(i,i), 0<=i < .}. This construction is important for the development of the theory of deflators on deformed structures. The paper also gives the most general definition of a deformed stochastic basis of the second kind with continuous time. Some important properties of this object are given.