Courses
in Stochastics in Spring
2007
Stefan
Geiss
Stokastiset
differentiaaliyhtälöt
(Stochastic
differential equations)
MATS351,
9 op (5ov), 50 h
Time and Place:
Monday
12-14 MaD 380
Tuesday
08-10 MaD 380
First lecture: 08/01/2007
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
-)
Ito's formula
-)
Stochastic differential equations
Literature:
[1]
I. Karatzas and A. Shreve: Brownian motion and
stochastic
calculus
[2]
D. Revuz and M. Yor: Continuous martingales and
Brownian
motion
Script: here
Exercises:
Problems
15/01/2007
Problems
22/01/2007
Problems
29/01/2007
Problems
05/02/2007
Problems
12/02/2007
Problems
19/02/2007
Problems
26/02/2007
Problems
05/03/2007
Problems
12/03/2007
Problems
19/03/2007
Problems
26/03/2007
Problems
02/04/2007
Christel Geiss
Probability
Theory 1
MATA261, 3ov (5
op), 34 h
Time
and Place:
Tuesday
12-14 MaD 381
Thursday
12-14 MaD 381
First lecture:
09/01/2007
Description:
Probability theory is used understand
random phenomena by mathematical means. In the course we will introduce
probability measures
and study their
properties. Then we will deal with random variables,
relate independence to product spaces, and consider the expected value
of a random variable. Finally, we will realise what is special about
the Gaussian distribution that it can be used to model, for example,
measuring
errors.
Probability Theory
1 is the basic course of the Stochastic Line, its
content is needed in all other stochastic courses.
Literature:
[1] A. Gut:
Probability: a graduate course (Springer)
Script: here
Exercises:
Problems
18/01/2007
Problems
25/01/2007
Problems
01/02/2007
Problems
08/02/2007
Problems
15/02/2007
Problems
22/02/2007
Problems
01/03/2007
Problems
08/03/2007
Problems
15/03/2007
topics for the test