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.
Lectures
|
Thu
|
11:00a.m.-12.30a.m. |
room 1.013 |
|
Thu
|
3:00p.m.-4:30p.m. |
room
1.115 |
|
|
|
|
| Exercises
(Irina Penner) |
Wed
|
1:15p.m.-2:45p.m.
|
room
3.008 |
Textbooks:
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
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