几类随机指数函数空间的应用

Since the new century, with the emergence of nonlinear problems in financial engineering, on which stochastic analysis is applied, we hope that variable exponent function spaces have some help in some nonlinear problems of financial engineering because of a good performance in solving some nonlinear problems of natural science and engineering. This project focuses on discussing properties of stochastic variable exponent function spaces further, and in this framework, solutions of several types of SPDEs with stochastic variable exponent growth are considered by theory of regularity structures.

进入新世纪以来，金融工程等随机分析应用领域中非线性问题的不断出现，基于变指数函数空间对解决在自然科学和工程技术中的一些非线性问题有着很好的表现，我们期待具有随机指数的变指数函数空间对解决在金融工程等领域出现的非线性问题会有所帮助。本项目将进一步讨论随机指数函数空间性质，以随机指数函数空间为框架，利用正则结构理论，考虑几类具有随机指数增长条件的随机偏微分方程解的问题。