A decoupling principle for Markov-modulated chains

Abstract Markov modulation has been widely employed in various fields of application, such as finance, economics, information and computer sciences, operations research, healthcare, and bio-medicines, whereas the additional modeling flexibility comes at the cost of demanding computation and complex inference procedure. The aim of this paper is to establish a decoupling principle for Markov-modulated chains, which enables one to represent an expectation on a Markov-modulated chain by a convergent sequence written on a set of ordinary continuous-time Markov chains. The proposed decoupling principle covers a large class of Markov-modulated chains, ranging from a variety of Markov-modulated processes to time-inhomogeneous models without time-discretization of the generator matrices, and has great potential for easing the computation around Markov-modulated chains.