Inhomogeneous time change equations for Markov chains and their applications

Abstract

In this paper we consider inhomogeneous time change equations (TCE) for Markov chains. We prove the existence and uniqueness of solution of the TCE and then study the influence of the time change on Markov consistency property and Markov structures of processes. In the first part we focus on time-changed Markov chains, whereas in the second part we use the TCE to change time in diffusion processes, obtaining regime-switching diffusions. This procedure is useful for applications in finance, where regime-switching diffusions are used to introduce stochastic volatility to the asset price model.