PROBABILISTIC METHODS IN MATHEMATICAL PHYSICS
Degree course:
Academic year when starting the degree:
2014/2015
Year:
3
Academic year in which the course will be held:
2016/2017
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:
Lebesgue integration theory, probability theory, partial differential equations
Assessment:
Voto Finale
Provide an introduction to the connections between some equations of mathematical physics and stochastic processes
Measure theory.
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.
1. Lecture notes
2. P. Baldi: Equazioni differenziali stocastiche e applicazioni. Pitagora Editrice
Borrowed from
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Degree course in: MATHEMATICS