Uniqueness and robustness of solution of measure-valued equations of nonlinear filtering

• 成果类型: Article
• 署名作者: Bhatt, AG; Kallianpur, G; Karandikar, RL
• 署名单位: University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987808
• 发表日期: 1995
• 页码: 1895-1938
• 关键词: Existence

摘要

We consider the Zakai equation for the unnormalized conditional distribution sigma when the signal process X takes values in a complete separable metric space E and when h is a continuous, possibly unbounded function on E. It is assumed that X is a Markov process which is characterized via a martingale problem for an operator A(0). Uniqueness of solution for the measure-valued Zakai and Fujisaki-Kallianpur-Kunita equations is proved when the test functions belong to the domain of A(0). It is also shown that the conditional distributions are robust.