Continuous and Discrete Stochastic Analysis

Periodo di svolgimento
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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.


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.

Obiettivi formativi

Goal of the lectures is to introduce students to basic topics of Probability theory and stochastic processes, useful in several fields and applications, including Mathematical Finance.

Riferimenti bibliografici

Notes of the teachers.