Mixing distributions on a Markov chain
Odd O. Aalen · Scandinavian Journal of Statistics · 1987
I consider a simple homogeneous, time-continuous Markov chain where the inten- sities are substituted by random variables (each being the product of a parameter and a mixing variable). The dynamic structure of the resulting process may be described by complete intensity functions given the entire past. I show how these functions can be expressed by means of the joint Laplace transform of the mixing variables. Some further properties of the process are also dis- cussed. I then consider various ways to construct non-negative multivariate mixing distributions with a known Laplace transform. Finally some computations are made for a two-state Markov chain.