87975 - ANALISI STOCASTICA 2

Learning outcomes

At the end of the course, the students know the fundamentals of stochastic calculus, of the theory of stochastic differential equations and the links with the theory of elliptic-parabolic and first order partial differential equations. They know how to apply the acquired knowledge to solve, also numerically, various types of problems inherent to some classical kinetic models of physics and other applications in finance, engineering, biology etc.

Course contents

The course is divided into two sections:

The goal of the first one is to complete and consolidate the knowledge acquired in the course Analisi Stocastica 1, regarding the theory of stochastic processes, of stochastic calculus, as well as their link with partial differential equations.

The second part of the course is aimed at introducing the student to a selection of topics, also presenting their connections to modern research problems in the field of stochastic calculus and its applications. Such topics include:

- Jump-diffusion processes and stochastic differential equations with jumps

- Backward stochastic differential equations

- Stochastic optimal control

- Introduction to stochastic partial differential equations

- Mean field particle systems, McKean-Vlasov stochastic equations, and mean field games

- Stochastic Langevin equation and Hörmander-type operators

- Introduction to numerical analysis for stochastic differential equations

 

Readings/Bibliography

Lecture notes, bibliographic references and additional material will be provided.

Teaching methods

Lectures on the board.

Assessment methods

Written test, and possibly oral test too. 

Teaching tools

Lecture notes and other material (codes, slides, etc.) showed in class will be shared with the students. 

Office hours

See the website of Stefano Pagliarani

See the website of Andrea Cosso