DISSIPATIVITY IN MEAN SQUARE OF STOCHASTIC REACTION DIFFUSION SYSTEMS

摘要：

It is by means of Lyapunov method that stochastic ordinary differential equations and stochastic functional differential equations have been studied intensively.However, for stochastic reaction diffusion equations, this useful technique seems to find no way out on account of the empty of its own Itos formula.To get over this difficulty, we will regard the integral of the considered trajectory with respect to spatial variables as the solution of the corresponding stochastic ordinary differential equations, via employing Itos formula under integral operator instead of directly applying Itos formula to Lyapunov functions in the case of stochastic ordinary differential equations, to aim at establishing the theory of dissipativity for Ito stochastic reaction diffusion systems.Some sufficient conditions for dissipativity and uniform dissipativity in mean square are given and this paper ends up with an example illustrating the obtained results.

关键词： Stochastic reaction diffusion systems Lyapunov function Ito differential formula Dissipativity In mean square

作者: YU-TIAN ZHANG QI LUO

作者单位: College of Mathematics and Physics, Nanjing University of Information Science & Technology, Nanjing College of Information and Control, Nanjing University of Information Science & Technology, Nanjing

会议类型: 国际会议

会议名称: 2007 International Conference on Machine Learning and Cybernetics(IEEE第六届机器学习与控制论国际会议)

会议地点: 香港

会议语种:英文

页码: 2639-2644

在线出版日期: 2007-08-19（万方平台首次上网日期，不代表论文的发表时间）