PLAN RADA SEMINARA ZA OKTOBAR 2002.

U narednom periodu na seminaru ce izlagati gosti iz inostranstva, Profesor Zoran Pop-Stojanovic (University of Gainsville, Florida, SAD), koji ce odrzati kratak kurs iz teorije martingala i Profesor Nikolaj Janev (Matematicki institut Bugarske Akademije nauka, Sofija, Bugarska), koji ce izloziti kratku teoriju i svoje rezultate iz teorije granajucih (branching) procesa. Takodje, nasa koleginica Rozsa Horvath Bokor (Madjarska) najavila je dolazak i ucesce na seminaru. O njenom saopstenju o statistici slucajnih procesa (koje bi bilo 13. ili 14. novembra) obavesticemo vas naknadno.

PAZNJA

Molimo da obratite paznju na datume i vremena odrzavanja seminara jer se razlikuju od uobicajenih.

Cetvrtak, 30. oktobar u 12 h.
dr Zoran Pop-Stojanovic:
Teorija martingala i neke primene u matematici finansija.

Na kursu ce biti izlozeni fundamentalni stavovi teorije martingala i semimartingala, kao i njihova veza sa stopping times. Bice razmotrene i neke vazne martingalne nejednakosti. Kako je moderna matematika finansija bazirana na teoriji martingala, na predavanjima ce se prikazati primena martingalne teorije u ovoj oblasti.

Cetvrtak, 30. oktobar u 14 h.
dr Nikolaj Janev:
Modelling of Stochastic Periodicity: Renewal, Regenerative and Branching Processes.

It is shown that some real stochastic phenomena can be considered as alternating renewal and regenerative processes. For these processes new limit theorems are obtained in the case when the tail distributions of the periods of regeneration are regularly varying at infinity (i.e. belong to the domain of attraction of stable laws). It will be demonstrated an application of the obtained Basis Regeneration Theorem in the field of branching processes with state-dependent immigration. Other possible applications will be discussed also.

Petak, 31. oktobar u 12 h.
dr Zoran Pop-Stojanovic:
Teorija martingala i neke primene u matematici finansija. Nastavak kursa

Cetvrtak, 30. oktobar u 14 h.

Zajednicki sastanak sa Odeljenjem za matematiku dr Nikolaj Janev:
Controlled Branching Processes and Statistical Inference for Branching Processes.

A review of the general theory will be presented. Some interesting particular cases will be also considered especially when the regularly varying functions play an important role in the limit behaviour. Some non-published results will be presented also. Non parametric estimation for the most important characteristic of some classes of branching processes is proposed. New limit theorems are obtained especially in the case when the processes start with a large number of ancestors. Computer simulations and estimations can be demonstrated.

Slobodanka Jankovic i Svetlana Jankovic
rukovodioci seminara