In this paper, we study the weak convergence of a sequence of Markov-modulated diffusion processes when the modulating Markov chain is ergodic and rapidly switching. We prove, in particular, its tightness property based on Aldous’ tightness criterion.

type="main" <p>This paper studies one-dimensional Ornstein–Uhlenbeck (OU) processes, with the distinguishing feature that they are reflected on a single boundary (put at level 0) or two boundaries (put at levels 0 and d  0). In the literature, they are referred to as reflected OU (ROU) and...</p>