Stability for generalized stochastic equations

Abstract

Similarly to generalized ordinary differential equations that comprise various types of classical deterministic equations, generalized stochastic equations (GSEs) were created to contain equations involving stochastic processes. The main goal of this paper is to investigate several types of stability and boundedness for non-autonomous GSEs by means of Lyapunov functionals. We also established existence–uniqueness results for maximal and global forward solutions of GSEs and applied our result to the Ornstein–Uhlenbeck process.