To strengthen the basic knowledge of Probability Theory (while making the class more homogeneous) by revisiting fundamental contents with a markedly formal approach. The aim of the course is to provide concepts, contents and tools that form the basis both for a more in-depth study of the theory and for an informed use of stochastic processes in applications.
Contents
Conditional expectations. Stopping times. Martingales and convergence results. Brownian motion and Brownian bridge. Some laws of Brownian motion. Analytical approach to Brownian motion. Stochastic integration. Itô formula and stochastic differential equations.
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