Fundamental knowledge of the theory of stochastic processes

general theory; random times; measurability; martingales with discrete time: convergence theorems, maximal inequalities; martingales with continuous time: path behaviour, regularization; Brownian motion, Poisson process; Markov processes;invariance prnciple; stochastic integration; foundations of stochastic diffenrential equations and Itô integral

The exact time of this lecture and the corresponding exercises will be fixed on Thu March 6th HS 15 at 9h00.

written and oral examination

Bauer, H.: Wahrscheinlichkeitstheorie

Neveu, J.: Martingales à temps discret

Karatzas, I.; Shreve, St.E.: Brownian motion and stochastic calculus

Rogers, L.C.G.; Williams, D.: Diffusions, Markov processes and martingales

Measure and probability theory