The course aims to provide an introduction to the theory of stochastic processes, particularly Markov processes, Brownian motion, and its connections with the heat equation.
Course Prerequisites
basics of probability and measure theory
Teaching Methods
Frontal lessons. In the lectures the theoretical notions are developed and the techniques necessary for the application of the theory to the solution of problems in Mathematical Physics are described.
Assessment Methods
Oral test which consists in verifying the ability to express oneself in correct mathematical language and to demonstrate some of the theorems encountered during the course.
Contents
Brownian motion. Wiener measure. Properties of Brownian trajectories. Markov processes. Markov semigroups and their generators. Diffusion processes. Probabilistic solution of the Dirichlet problem for the Laplace equation. Probabilistic solution of the Cauchy-Dirichlet problem for the heat equation. Feynman-Kac formula. Stochastic calculus, Ito's formula, stochastic differential equations
Course Language
English
More information
to make an appointment write to posilicano@uninsubria.it
