A filtering problem with a small nonlinear term
作者:
Jean Picard,
期刊:
Stochastics
(Taylor Available online 1986)
卷期:
Volume 18,
issue 3-4
页码: 313-341
ISSN:0090-9491
年代: 1986
DOI:10.1080/17442508608833412
出版商: Gordon and Breach Science Publishers, Inc
关键词: Nonlinear filtering;approximation;asymptotic expansions
数据来源: Taylor
摘要:
In this paper, we consider a filtering problem where the signalXtsatisfies a slightly nonlinear stochastic differential equation and we want to obtain estimates ofXt. To this end, we decompose the nonlinearity with two techniques—a deterministic one and a stochastic one—and this leads us to two sequences of estimates which can be computed by solving finite dimensional equations. We want to compare their performances: we solve this problem in most cases if we restrict ourselves to sufficiently small times t and we give conditions which permit to conclude also for larger times
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