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

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