Continuous and Discrete Stochastic Analysis
Prerequisiti
The lectures are addressed to PhD students, mainlyoriented to applications. Previous knowledge of the basicsof Probability are very useful, although not strictlynecessary. No previous knowledge of stochasticprocesses is required
Programma
Foundations and elementary examples: Probability space,conditional probability and independence, expectedvalues and main results of calculus, discrete andcontinuous examples. Conditional expectation. Main limittheorems.Elements of theory of stochastic processes. Brownianmotion, Kolmogorov regularity theorem, quadraticvariation.Elements of martingale theory. Examples.Elements of stochastic integration and stochasticdifferential equations. Links with Partial DifferentialEquations.Continuous time Markov chains: some elements oftheory, infinitesimal generators, useful rules. Randomwalks. Links between discrete and continuous theory.
Obiettivi formativi
Goal of the lectures is to introduce students to basictopics of Probability theory and stochastic processes,useful in several fields and applications, includingMathematical Finance.
Riferimenti bibliografici
Notes of the teachers.