ABSTRACT
The classical theory of stochastic differential equations deals with processes of the Itô type, driven by an external Wiener process. More recently, there has been interest in equations driven by a more general Markov process, which may be a jump process or a diffusion process. It is the purpose of the present paper to outline a unified framework for these models as applied to questions of stochastic Lyapunov stability. Related unified models in the linear case were studied in the context of large deviation theory by Arnold and Kliemann [5].
