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
韩捷 1陈光淦 1雷婷1
作者信息
- 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
- 折叠
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Wong-Zakai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.
Abstract
This work is concerned with a stochastic evolutionary equation with a mul-tiplicative noise.Verifying the convergence from the solution of the stochastic evolu-tionary equation to one of its Wong-Zakai approximation and applying the exponential martingale argument,the Kallianpur-Striebel formula and Itô 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Key words
stochastic evolutionary equation/Wong-Zakai approximation/nonlinear filter/observation system with colored noise引用本文复制引用
出版年
2025
NETL
NSTL
万方数据