**Seminar on Stohastics**

**PROGRAM**

Matematicki institut SANU

Kneza Mihaila 35/1

__PLAN RADA SEMINARA ZA OKTOBAR 2004.__

__Cetvrtak, 28. oktobar u 12 h.__

* *

Lectures on Brownian Motion Process and its Applications

The series of lectures will present the construction of the Brownian Motion process in ${R}^{d}$ and show its Markov, and Strong Markov Properties. Basic properties of the Brownian Motion process, such as local properties of its paths, Blumenthal 0-1 Law and its ramifications, connection to Dirichlet problem, and harmonic functions, as well as its connection with the Martingale Theory, will be presented.

__Petak, 29. oktobar u 12 h.__

* Profesor Zoran R. Pop-Stojanovic (Department of Mathematics, University of Florida, Gainesville, FL 32611) *

Reverse Markov Inequality, and BMO Functions

The Reverse Markov Inequality obtained jointly with J. Sokolowski i M. Rao, will be presented. Its various applications and its connection with the BMO Martingales, will be presented.

OBAVESTENJE

Profesor Zoran Pop-Stojanovic ce tokom svog boravka u Beogradu odrzati predavanja i u novembru sa sledecim temama:

3. Linear Stochastic Filtering

Bucy-Kalman Filtering Theory will be presented, when both, the system evolution, and its observations, are given by SDEs.

4. Building Portfolios via SDEs

The methods from the SDEs will be presented which are used for building investment portfolios in complete markets.

Predavanja ce se drzati tokom cetri dana, 28. i 29. oktobra i 11. i 12. novembra. Svakog od tih dana bice odrzana po dva predavanja: prvo sa pocetkom u 12h, a drugo sa pocetkom u 15h.

Slobodanka Jankovic i Svetlana Jankovic

rukovodioci seminara