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Teacher
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CANDELLERO ELISABETTA
(syllabus)
Brownian motion: definition and property of BM, continuity and non-differentiability of the trajectories. Markov property, strong Markov property and reflection principle. Multi-dimensional BM, harmonic functions and Dirichlet problem. Skorokhod embedding and Donsker invariance principle.
Stochastic integration: Paley-Wiener-Zygmund integral. Stochastic integral, Ito's formula and applications. Stochastic differential equations, Theorem of existence and uniqueness of solutions of SDEs. Exercises.
(reference books)
Brownian Motion (Moerters and Peres): http://www.mi.uni-koeln.de/~moerters/book/book.pdf
An introduction to Stochastic Differential Equations (Evans)
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Università Roma Tre