Exponential stability of stochastic differential equations

This unique, self-contained reference presents a systematic study of current developments in stochastic differential delay equations driven by nonlinear integrators - detailing various exponential stabilities for stochastic differential equations and large-scale systems. Reviewing the basic principles of stochastic processes, Exponential Stability of Stochastic Differential Equations illustrates the practical use of stochastic stabilization, stochastic destabilization, stochastic flows, and stochastic oscillators in numerous real-world situations . . . establishes a new theory of the existence and uniqueness of the solution for a stochastic differential equation driven by a nonlinear integrator under a weaker condition than that of Lipschitz . . . supplies the generalized Gronwall inequality and Bhiari inequality . . . introduces C-semimartingales with spatial parameters and the stochastic integrals based on them . . . demonstrates the manifestations of the Lyapunov method . . . examines the concept of stochastic bounded integral contractors in the context of stochastic differential equations . . . analyzes the classical Ito integral and Ito formula . . . discusses Cauchy-Maruyama's and Carathedory's approximate solutions to stochastic differential equations . . . and more.