Examination procedure
Written and oral exam
Prerequisites
The lectures are addressed to PhD students, mainly oriented to applications. Previous knowledge of the basics of Probability are very useful, although not strictly necessary. No previous knowledge of stochastic processes is required.
Syllabus
Foundations and elementary examples: Probability space, conditional probability and independence, expected values and main results of calculus, discrete and continuous examples. Conditional expectation. Main limit theorems.
Elements of theory of stochastic processes. Brownian motion, Kolmogorov regularity theorem, quadratic variation.
Elements of martingale theory. Examples.
Elements of stochastic integration and stochastic differential equations. Links with Partial Differential Equations.
Continuous time Markov chains: some elements of theory, infinitesimal generators, useful rules. Random walks. Links between discrete and continuous theory.
Bibliographical references
Notes of the teachers.