general theory; types of stochastic processes, path properties, filtrations and stopping times, Markov Processes: transition function, homogeneity, Chapman-Kolmogorov equations, Markov chains: transition matrices, successors, communicating states, period, recurrence properties, absorption, Markov chains in continuous time: infinitesimal parameters, conservative chains, Kolmogorov differential equations, embedded discrete Markov chain, bitrh-and death processes, explosion, regularity, minimal solution; general theory of Markov processes: path properties, transition oprators, resolvent, infinitesimal operator, Hille-Yosida theorem; martingales: definition, semimartingales, transformations, optional stopping, optional selection, maximum inequality, martingale convergence theorem, Doob-Meyer decomposition; stochastic calculus: Ito integral, Ito's formula, stochastic differential equations: existebce and uniqueness theorem

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