一类随机发展方程有效滤波的Wong-Zakai逼近  

A Wong-Zakai Approximation for Effective Filtering of a Class of Stochastic Evolutionary Equation

作　　者：韩捷 陈光淦 雷婷 HAN JIE;CHEN GUANGGAN;LEI TING(School of Mathematical Sciences,and Visual computing and virtual reality Key Laboratory of Sichuan Province,Sichuan Normal University,Chengdu 610068,China)

机构地区：[1]四川师范大学数学科学学院,可视化计算与虚拟现实四川省重点实验室,成都610068

出　　处：《应用数学学报》2025年第1期139-151,共13页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(12171343);四川省科技计划(2022JDTD0019)资助。

摘　　要：研究一类带有乘性噪声的随机发展方程.在获得随机发展方程的解收敛到WongZakai逼近方程的解后,使用指数鞅技术、Kallianpur-Striebel公式和Ito公式,证明随机发展方程及Wong-Zakai逼近方程在带有色噪声的观测系统中所产生的非线性滤波的收敛行为,进一步得出具体收敛速率.This work is concerned with a stochastic evolutionary equation with a multiplicative noise.Verifying the convergence from the solution of the stochastic evolutionary equation to one of its Wong-Zakai approximation and applying the exponential martingale argument,the Kallianpur-Striebel formula and Ito formula,we prove that the nonlinear filter generated by the stochastic evolutionary equation converges to one generated by its Wong-Zakai approximation in the observation system with colored noise.

关 键 词：随机发展方程 Wong-Zakai逼近 非线性滤波 带有色噪声的观测系统 

分 类 号：O211.6[理学—概率论与数理统计] O175.2[理学—数学] O211.4