Stochastic Control with Partial Observation and Approximation Techniques.
Interim rept. no. 1.
INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE ROCQUENCOURT (FRANCE)
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Two different approaches have been investigated for the MLE of partially observed diffusions. Some formulas given have been clarified, and it has been shown that smoothing is necessary to make the EM algorithm approach efficient. On the other hand, formula have been given in terms of SPDE for the computation of the original log-likelihood ratio and its gradient. As might have been noticed, expressions related to the direct approach are given in terms of unnormalized conditional densities, whereas in the EM algorithm approach normalized conditional densities have been used. As a consequence, it does not appear so clearly, except for some particular cases, already considered, that the EM algorithm is faster than the direct approach. This should be investigated on numerical examples.
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