Data-driven inference for stochastic dynamics

Module 1: Stochastic Dynamics <br> The module treats the basic theory and practice of stochastic dynamics. Theoretical key concepts include: stochastic integral, Itô formula, stochastic differential equations (SDE), existence and uniqueness of strong solutions, martingales, Markov property. Practical implementation (in R or Python) of Euler-Maruyama and Milstein methods for numerical solution of SDEs. Module 2: Estimation for SDEs and Markov Chains <br> The module covers the theory of maximum likelihood and quasi-maximum likelihood estimations as well as Bayesian inference. Practical implementation (in R or Python) of Markov Chain Monte Carlo methods and the Metropolis-Hastings algorithm and its variants. Module 3: Bayesian Filtering <br> The module treats the theory and practice of filtering. Theoretical key concepts include Kalman filters, extended Kalman filters, particle filters, and nonlinear filtering. Practical implementation (in R or Python) of filters with various datasets and models.