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ANALYTIC AND PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS II

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2024/2025
Year: 
2
Academic year in which the course will be held: 
2025/2026
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: 

basics of probability and measure theory

Final Examination: 
Orale

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.

Assessment: 
Voto Finale

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.

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

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.

to make an appointment write to posilicano@uninsubria.it

Professors

POSILICANO ANDREA

Borrowers