随机微分系统的耗散性

Dissipativity of Stochastic Differential Systems

提出了有关Ito型随机微分系统耗散性理论的新概念:按模耗散、按模等度耗散和按模一致耗散,并利用Lyapunov方法,借助于Ito微分公式沿着Ito型随机微分系统的解对所构造的Lyapunov函数求导数,给出了Ito型随机微分系统有关按模耗散理论的一些代数判据,获得了与确定性常微分系统耗散性理论相对应的结论,最后的算例证明了该方法的有效性和可行性。

Some new conceptions are presented about the dissipativity theory of Ito stochastic differential systems as follows., dissipativity in module, equi-dissipativity in module and uniform dissipativity in module. Moreover, using Ito differential formula to the constructed Lyapunov function along solutions of Ito stochastic differential systems, Lyapunov method is adopted to set up the fundamental theory of dissipativity in the module corresponding to the theory on the dissipativity of deterministic ordinary differential systems. Finally, some examples show the feasibility and the validity of the method.