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IMA Journal of Mathematical Control and Information 1984 1(2):129-140; doi:10.1093/imamci/1.2.129
© 1984 by Institute of Mathematics and its Applications
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Parameter Estimation for Observed Diffusions in Manifolds

S. K. NG, P. E. CAINES and H. F. CHEN

Department of Electrical Engineering, McGill University Montreal, P.Q. Canada
Department of Electrical Engineering, McGill University Montreal, P.Q. Canada Institute of Systems Science Beijing, China

Following the procedure described by Elworthy (1982) and Ikeda & Watanabe (1981) we construct the solution of stochastic differential equations (SDEs) in manifolds. We take such SDEs to describe parametrized completely observed stochastic systems and manifold-valued state processes. The likelihood function for the system parameter is computed by two methods: the first applies to the case of parallelizable manifolds; the second applies to the general case, here the solution of the system SDE is constructed in the orthonormal frame bundle of the manifold. Two examples are given.


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