Detection and Filtering
In both the detection problem and the filtering problem a sample path from some random process O is observed. In the detection problem, it is postulated that one of two known probability measures P or PO is given on the underlying space (Ω, A). Presumably the distribution of the observed process is different under P and PO. The problem is to intelligently guess which of the two measures is in effect, on the basis of the observation. In the filtering problem a random process ξ, which may be a coordinate of some other random process, is given and the problem is to produce at each time t an estimate of ξ t .
KeywordsStochastic Differential Equation Detection Problem Counting Process Local Martingale Predictable Process
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