Stochastic Analysis - Einzelansicht

The Monday lectures begin at 08:45.

Participants in this course are expected to have learned the following material in previous mathematics courses.

Measure theory: measure spaces, sigma-algebras, measurable functions, null sets, Fubini-Tonelli theorem, dominated convergence theorem, monotone convergence, Fatou's lemma, etc.

Measure-theoretic probability theory: probability spaces, expectations conditioned on sigma-algebras, uniform integrability of random variables, different modes of convergence of random variables, characteristic function / Fourier transform, Borel-Cantelli lemmas, weak convergence, etc.
 
Analysis: right- and left-continuous functions, limits, limit inferior and limit superior, Banach spaces, Hilbert spaces, L^p spaces, completeness, suprema and infima of sets, Holder continuity, convergence, epsilon-delta proofs, dense subsets, Lebesgue-Stieltjes integrals, differential and integral calculus, etc.

Participants in this course are expected to have significant experience in understanding and creating rigorous mathematical proofs.

Elements of martingale theory in discrete time and in continuous time, Brownian motion, stochastic integrals, Ito's formula, stochastic differential equations

The target audience of this course are students in the M.Sc. Mathematics who satisfy the prerequisites, and who have significant experience in writing rigorous proofs and applying results from measure-theoretic probability theory.