A note on independence copula for conditional markov chains

Abstract

Given a family (Y k, k = 1, 2, …, N) of conditional Markov chains, we construct a conditional Markov chain X = (X1, …, X N) such that X k, k = 1, 2, …, N, are conditional Markov chains, which are conditionally independent given the information contained in some filtration F, and such that for each k the conditional law of X k coincides with the conditional law of Y k. This is a new result that can be used to model different phenomena such as the gating behavior of multiple ion channels in a membrane patch, or credit ratings migrations.