Humboldt Universität zu Berlin
Institut für Mathematik
Homepage Prof.Küchler



Winter term 2007/2008

BMS Basic Course „Stochastic Processes“ / Stochastik II

Course description:

characteristic functions of random vectors, Gaussian distributions in Rn, finite-dimensional distributions,
classification of stochastic processes:
Gaussian, Brownian motion, Brownian bridge, processes with independent increments, Poisson processes, compound Poisson processes,  Levy processes, Levy characteristics, stationary processes, ergodic theorems, Markov processes and transition functions

properties of trajectories of stochastic processes, conditional Expectations, Martingales, supermartingales, Doobs decomposition, Upcrossing theorem, convergence a.s. theorem,  law of large number, central limit theorem,uniformly integrability, backwards martingales, convergence in L1,
Markov chains with discrete time, Markov chains with continuous time, weak convergence, Donskers invariance priciple, properties of the Brownian motion, geometric Brownian motion,
applications in Mathematical Finance


The course will take place in Campus Adlershof, Johann von Neumann-Haus, Rudower Chaussee 25.

11:00a.m.-12.30a.m. room 1.013

3:00p.m.-4:30p.m. room 1.115

Exercises   (Irina Penner) Wed 
 room 3.008


Gihman, I.L., Skohorod, A.V.: The Theory of Stochastic Processes I-III.
Additional literature will be announced in the beginning of the course.

Office Hours:

wednesday, 1:00-3:00 p.m., RUD 25, 1.202, Tel. 2093-5811

last modification: 10/04/2007, Katja Krol