The course intends to provide an in-depth knowledge of stochastic processes, and in particular of Markovian processes, both from a theoretical and an applied point of view.
Some general probabilistic tools and topics will be discussed along the course, such as Poisson measures, coupling techniques, large deviation principles, infinite divisible laws and convergence of measures (laws of processes). Then, advanced applications related to processes on discrete spaces and on continuous spaces will be shown.
This will include branching processes, interacting particle systems, genetic models (the Wright-Fisher diffusion), and some selected applications in the context of partial differential equation (the Dirichlet problem and the martingale problem).
Some general probabilistic tools and topics will be discussed along the course, such as Poisson measures, coupling techniques, large deviation principles, infinite divisible laws and convergence of measures (laws of processes). Then, advanced applications related to processes on discrete spaces and on continuous spaces will be shown.
This will include branching processes, interacting particle systems, genetic models (the Wright-Fisher diffusion), and some selected applications in the context of partial differential equation (the Dirichlet problem and the martingale problem).
- Docente: Alessandra Bianchi