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 = (X 1, …, 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 \(\mathbb{F}\), 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.