“…Inspired by problems of model complexity in random environments, in which both structural changes and sudden changes of parameters as well as large fluctuations coexist and are intertwined, this paper study regime-switching jump diffusion processes. The quantitative properties of these systems have greatly expanded over the previous few years, with most results making a connection between the control theory and the qualitative dynamics or long-time behavior of the associated dynamical system, see, for example, [5,17,18,19,20,21,22,23,25] and references therein.…”