This talk deals with simulation and inference methods for deterministic and random dynamical systems described by differential equations, reliable approximations and applications. Focused on the Local Linearization approach, a variety of integration and estimation methods for various classes of differential equations are presented. Convergence, stability, preservation of dynamical properties and computational efficiency of the integrators are described. Estimation methods from complete or partial discrete observations contaminated with noise are presented. This includes properties of the estimators (such as bias, consistency, efficiency, etc.) as well as the feasibility of computationally efficient implementations. Finally, various practical problems in neurosciences, finance, epidemiology and others where the application of these methods has been relevant are listed.
*Texto informado pelo autor.
Juan Carlos Jimenez is currently Senior Professor at the Department of Interdisciplinary Mathematics of the Institute of Cybernetic, Mathematics and Physics in Havana. He has a Ph.D. in Mathematics and a B.S. in Nuclear Physics from Havana University. His main research interest is the simulation and identification of continuous-time dynamical system and its applications, a field in which he has actively worked in the last two decade