Computable infinite-dimensional filters with applications to discretized diffusion processes

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• 作者：Mireille Chaleyat-Maurel and Valentine Genon-Catalot
• 关键词：Stochastic filtering ; Diffusion processes ; Discrete time observations ; Hidden Markov models ; Prior and posterior distributions
• 刊名：Stochastic Processes and their Applications
• 出版年：2006
• 期刊代码：57_03044149
• 类别：mt
• 出版时间：October 2006
• 卷：116
• 期：10
• 页码：1447-1467
• 文件大小：373 K

摘要

Let us consider a pair signal–observation RKBGD-1&_mathId=mml1&_user=10&_cdi=5670&_rdoc=7&_handle=V-WA-A-W-E-MsSAYVW-UUA-U-AAZCWWZEVB-AAZWYUDDVB-VWAZDUUB-E-U&_acct=C000050221&_version=1&_userid=10&md5=2ad68352d98f277703a9e4af41197585" title="Click to view the MathML source">((x_n,y_n),n≥0) where the unobserved signal (x_n) is a Markov chain and the observed component is such that, given the whole sequence (x_n), the random variables (y_n) are independent and the conditional distribution of y_n only depends on the corresponding state variable x_n. The main problems raised by these observations are the prediction and filtering of (x_n). We introduce sufficient conditions allowing us to obtain computable filters using mixtures of distributions. The filter system may be finite or infinite-dimensional. The method is applied to the case where the signal x_n