Christel Geiss
An introduction into probability theory
MAT283, 3 ov, 34 h
Time and Place: Monday 12-14 MaD 381
Tuesday 14-16 MaD 381
First lecture: 08/09/2003
Description: Probability theory is the starting point to
understand
many random phenomena. How one can define probability properly?
What are random variables? And why is it correct if one uses a
Gaussian distribution to model measuring errors?
Contents of the lecture:
-) Probability spaces
-) Some special distributions
-) Random variables
-) Lebesgue integral
-) Sequences of random variables
Literature:
P. Billingsley: Probability and measure (Wiley)
A.N. Shiryaev: Probability (Springer)
D. Williams: Probability with martingales (Cambridge)
Exercises:
Problems
15/09/2003
Problems
22/09/2003
Problems
29/09/2003
Problems
06/10/2003
Problems
13/10/2003
Problems
20/10/2003
Problems
27/10/2003
Problems
03/11/2003
Problems
10/11/2003
Topics:
Tests
12/11/2003 and 03/12/2003
Stefan Geiss
Stokastiset differentiaaliyhtälöt
(Stochastic differential equations)
MAT359, 5 ov, 50 h
Time and Place: Monday 10-12 MaD
381
Wednesday 10-12 MaD 381
First lecture: 08/09/2003
Description: Stochastic differential equations are a fundamental
tool
in mathematics and in applications. Given a Brownian motion W=(W_t)_{t\ge
0},
a stochastic differential equation reads as
dX_t = a(t,X_t) dt + b(t,X_t) dW_t.
The solution should be a stochastic process (X_t)_{t\ge 0}. But
what
is the meaning of this equation? Or going one step back: what is
a
Brownian motion? Or, if we know this: what are the solutions, are
they
unique, what properties do they have? The course intends to answer
(at least some of) the questions.
Contents of the lecture:
-) Brownian motion
-) Stochastic integrals
-) It\^o's formula
-) Stochastic differential equations
Literature:
I. Karatzas and A. Shreve: Brownian motion and stochastic calculus
D. Revuz and M. Yor: Continuous martingales and Brownian motion
Exercises:
Problems
15/09/2003
Problems
22/09/2003
Problems
06/10/2003
Problems
13/10/2003
Problems
20/10/2003
Problems
27/10/2003
Problems
03/11/2003
Problems
10/11/2003
Problems
17/11/2003
Problems
24/11/2003
Problems
01/12/2003