Parameter Estimation for Observed Diffusions in Manifolds

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