Introduction to stochastic dynamical systems

We intend in the first two lectures to review the main introductory topics on stochastic analysis: martingales, Markov process, Brownian motion, Itô formula, stochastic differential equation and stochastic flow. In the last two lectures we show applications of stochastic calculus in geometry and dynamical systems, including stochastic processes in Lie groups, isometric decomposition of stochastic flows in Riemannian manifolds, and others.