Many problems in real life require the treatment of systems in which continuous dynamics and discrete events coexist. We present a survey of some of our recent work on such systems. In the setup, the discrete event is given by a random process taking values in a discrete set, and the continuous component is the solution of a stochastic differential equation. Seemingly similar to the usual random differential equations, the processes have a number of salient features distinctly different from diffusion processes. After providing motivational examples arising from wireless communications, identification, finance, singular perturbed Markovian systems, manufacturing, and consensus controls, we present necessary and sufficient conditions for the existence of unique invariant measure, stability, stabilization, and numerical solutions, and control and game problems.

殷刚, 韦恩州立大学(Wayne State University)教授，主要从事随机系统及应用的研究。于1987年加入韦恩数学系，现任该校 Distinguished Professor, 被选为IEEE Fellow (class 2002), SIAM Fellow (class 2015),  IFAC Fellow (class 2014-2017)。