Courses in Stochastics in Spring 2009



Stefan Geiss

Stokastiset differentiaaliyhtälöt 1 ja 2
(Stochastic differential equations 1 and 2)
MATS352, 5 op (3ov), 26 h
MATS353, 4 op (2ov), 24 h

Time and Place
Monday : 12-14 MaD 380
Tuesday : 08-10 MaD 380
First lecture : 12/01/2009

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

Exercises

Christel Geiss

Todennäköisyysteoria 1
(Probability Theory 1)
MATA261, 5 op (3ov), 30 h

Time and Place
Tuesday : 12-14 MaD 381
Thursday : 12-14 MaD 381
First lecture : 13/01/2009

Description: To describe and understand random phenomena by mathematical means one uses probability theory. 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 Exercises