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ANALYTIC AND PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS B

Degree course: 
Corso di Second cycle degree in MATHEMATICS
Academic year when starting the degree: 
2023/2024
Year: 
1
Academic year in which the course will be held: 
2023/2024
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 theory and of 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, in particular to Markov processes, to the Brownian motion and its connession with the heat equation. The result to be achieved at the end of the course is that the student knows how to use the basic techniques of the theory of stochastic processes, having also developed a good intuition on the meaning of the concepts learned.

Brownian motion, the Wiener measure. Properties of the Brownian paths. Markov processes. Markov semi-groups and their generators. Diffusion processes. Brownian motion and harmonic functions, the probabilistic solution of the Dirichlet problem for the Laplace equation. The Feynman-Kac formula. Stochastic calculus, Ito’s formula, stochastic differential equations.

Brownian motion, the Wiener measure. Properties of the Brownian paths. Markov processes. Markov semi-groups and their generators. Diffusion processes. Brownian motion and harmonic functions, the probabilistic solution of the Dirichlet problem for the Laplace equation. The Feynman-Kac formula. Stochastic calculus, Ito’s formula, stochastic differential equations.

Convenzionale

Frontal lessons: 64 hours. 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