Domain Theory in Stochastic Processes

We establish domain-theoretic models of nite-state discrete stochastic processes, Markov processes and vector recurrent iterated function systems. In each case, we show that the distribution of the stochastic process is canonically obtained as the least upper bound of an increasing chain of simple valuations in a prob-abilistic power domain associated to the process. This leads to various formulas and algorithms to compute the expected values of functions which are continuous almost everywhere with respect to the distribution of the stochastic process. We prove the existence and uniqueness of the invariant distribution of a vector recurrent iterated function system which is used in frac-tal image compression. We also present a nite algorithm to decode the image.