Exponential Stability Of It(?) Stochastic Differential Equation And Applications

With the development of the science and technology, people have attached very great importance to effects of stochastic factor on the system day by day. Stochastic differential equation (SDE) is a marginal subject, which is a combination of probability theory and ordinary differential equation. Since Ito published"Theory of Stochastic Differential Equations"(1961), more and more scientific theory workers and applied technical workers have paid much attention to it. The theory of SDE which is based on the certain differential equation and stochastic process, is growing especially fast and its application is also more and more extensive. It is mainly be applied to system science, engineering control, ecology, etc. In these newly arisen science techniques, large number of question about SDE are appeared, such as control problem under the stochastic interference, the filter wave within the communication technique problem, the question about the sonar probes into submarine, the establishment problem of living creature–mathematics model. They depend on research and resolve of SDE.The important meaning of stability is imaginable. From a small specific control system to a big social system, financial system, ecology system, etc. It is appeared under the various accidental or continuous disturb. After bearing this interference, system is uncertain to keep to circulate or work appearance and is unlikely to lose control or sway, so the stability of SDE have important theories meaning with extensive applied background.