The filtered martingale problem
The filtered martingale problem
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过滤鞅问题
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
A. Moro
中科院分区：
文献类型：
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作者：
T. Kurtz;G. Nappo;A. Moro
设X是一个马尔可夫过程，它刻画了一个具有生成元A的鞅问题的解，Y是一个相关的观测过程。给定Y到时间t的观测值X(T)的条件分布t满足一定的鞅性质，并且证明了任何具有适当的鞅性质的概率测值过程都可以解释为X对于某一观测过程的条件分布.特别地，如果对于某种可测映射，Y(T)=(X(T))，则X(T)的条件分布被刻画为滤子鞅问题的解。对于被认为是概率-测度过程的条件分布，原鞅问题的唯一性蕴含着过滤鞅问题的唯一性，而条件分布的唯一性又意味着条件分布的马尔可夫性。其他应用包括马尔可夫映射定理和滤波方程的唯一性。MSC 2000学科分类：60J25、93E11、60G35、60J35、60G44
Let X be a Markov process characterized as the solution of a martingale problem with generator A, and let Y be a related observation process. The conditional distribution t of X(t) given observations of Y up to time t satisfies certain martingale properties, and it is shown that any probability-measure-valued process with the appropriate martingale properties can be interpreted as the conditional distribution of X for some observation process. In particular, if Y (t) = (X(t)) for some measurable mapping , the conditional distribution of X(t) given observations of Y up to time t is characterized as the solution of a filtered martingale problem. Uniqueness for the original martingale problem implies uniqueness for the filtered martingale problem which in turn implies the Markov property for the conditional distribution considered as a probability-measure-valued process. Other applications include a Markov mapping theorem and uniqueness for filtering equations. MSC 2000 subject classifications: 60J25, 93E11, 60G35, 60J35, 60G44