ISTITUZIONI DI FISICA MATEMATICA
Degree course:
Corso di First cycle degree in MATHEMATICS
Academic year when starting the degree:
2019/2020
Year:
3
Academic year in which the course will be held:
2021/2022
Course type:
Compulsory subjects, characteristic of the class
Credits:
8
Period:
Second semester
Standard lectures hours:
64
Detail of lecture’s hours:
Lesson (64 hours)
Requirements:
The contents of the course ANALYTIC AND PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS A
oral examination
Assessment:
Voto Finale
The course aims to provide an introduction to the theory of continuous-time stochastic processes, in particular to the connection between Brownian motion and the heat equation
Brownian motion. The Wiener measure. Properties of the Brownian paths. Markov processes. Markov semi-groups 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. The Feynman-Kac formula. Stochastic calculus,stochastic differential equations
Notes provided by the lecturer
Frontal lessons