STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Registracija za učešće na seminaru je dostupna na sledećoj stranici:
https://miteam.mi.sanu.ac.rs/asset/wNBdwnywxpQb9RAEH
Ukoliko ste već registrovani predavanje možete pratiti na sledećem linku (nakon što se ulogujete):
https://miteam.mi.sanu.ac.rs/asset/cQQHaumdsFimvZXQB
Predavanja možete pratiti na daljinu preko stranice:
https://miteam.mi.sanu.ac.rs/call/cQQHaumdsFimvZXQB/5KxeeGJKug5sAYTkxxi-Dya7hOyXwzVIgcHdH8EQUkP

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Plan rada seminara Stohastika sa primenama za FEBRUAR 2025.

Četvrtak, 13.02.2025. u 11:00, Online
Jordan M. Stoyanov, Bulgarian Academy of Sciences and Shandong University
MOMENTS AND CUMULANTS IN PROBABILITY AND STATISTICS
For modelling real or abstract random phenomena, we use a variety of distributions, of any kind. In general, and for specific classes of distributions, we are interested in fundamental properties expressed in simple terms such as moments and/or cumulants (semiinvariants).
In order to address the diverse interests of the attendees (not possible to do this completely and at once), I will carefully choose and present important results about distributions in terms of their moments/cumulants.
One topic we are going to discuss is the moment-determinacy. I will describe a general picture and explain why under some conditions a distribution is M-determinate, while under other conditions it is M-indeterminate. The same, in terms of the cumulants. Some properties are valid only under determinacy. Then, we will discuss limit theorems in which the limit distribution is normal (remember the CLT established by Chebyshev and Markov). A surprising general result will be presented with a (nonconventional) limit, a bounded random variable. You will see how efficient the cumulants can be.
All results will be illustrated by specific continuous and/or discrete distributions and statements which sometimes look (at least) a little surprising.
If time permits, I will briefly discuss moment properties of stochastic processes, in particular, of the solutions of SDEs.

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Četvrtak, 27.02.2025. u 11:00, Online
Slađana Dimitrijević, Prirodno-matematički fakultet, Kragujevac
UZROČNOST I OČUVANjE NEKIH BITNIH OSOBINA SLUČAJNIH PROCESA
Koncept uzročnosti u neprekidnom vremenu unutar prostora verovatnoća sa filtracijom, koji se zasniva se na Grangerovoj definiciji uzročnosti, biće prosiren na slučaj kada se neprekidno vreme zameni vremenom zaustavljanja. Zatim će biti prikazano kako dati koncepti uzročnosti utiču na očuvanje nekih važnih osobina stohastičkog procesa u slučajevima kada se filtracija povećava, kao što su martingalnost, opcionalnost i predvidljivost. Takođe, biće ukazano na povezanost datog koncepta uzročnosti i opcionalnih i predvidljivih projekcija stohastičkih procesa koje igraju važnu ulogu u opštoj teoriji stohastičkih procesa. Neki rezultati pokazuju da (samo)uzročnost implicira nerazlikovanje opcionalnih (predvidljivih) projekcija slučajnih procesa u odnosu na razmatranu filtraciju i povećanu filtraciju.

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