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):
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Predavanja možete pratiti na daljinu preko stranice:
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Plan rada seminara Stohastika sa primenama za MART 2024.

Četvrtak, 07.03.2024. u 11:00, Online
Jordan M. Stoyanov, Bulgarian Academy of Sciences and Shandong University
CHARACTERIZATIONS OF PROBABILITY DISTRIBUTIONS: A BUNCH OF OLD AND NEW RESULTS
It is a classical problem for any specific distribution, say F, to find a property which is valid only for F. This is a characterization problem with a characterizing property. Well-known are classical results for popular distributions such as normal, Poisson, exponential, gamma, etc. (Cramer, Raikov, Polya, Bernstein, Skitovich-Darmois). The work on such problems is going on and some new very recent results will be reported.
We can also ask whether or not a distribution is uniquely determined by its moments, assuming they are all finite. This is one of the fundamental questions in the classical moment problem (Chebyshev, Markov, Stieltjes). Besides well-known results (Cramer, Hausdorff, Carleman, Hardy, Krein, Lin, rate of growth of moments), some very recent results on M-(in)determinacy of distributions will be presented.
All results will be illustrated by specific continuous and/or discrete distributions by statements which sometime are (at least) a little surprising. In particular, we will exhibit explicit SDEswhose solutions have prescribed moments. Challenging open questions will be outlined.

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Četvrtak, 21.03.2024. u 11:00, Online
Danijela Milenković, Farmaceutski fakultet, Beograd
REŠAVANJE JEDNODIMENZIONALNIH STOHASTIČKIH DIFERENCIJALNIH JEDNAČINA VIKOVOG TIPA
Standardni pristup u rešavanju stohastičkih diferencijalnih jednačina podrazumeva korišćenje Itovog kalkulusa. Neretko se dešava da se pomoću Itovog pristupa jednačine ne mogu rešiti ili se može samo utvrditi da postoji jedinstveno rešenje posmatrane jednačine ali se ono ne može eksplicitno izračunati. Na ovom predavanju pokazaćemo drugi pristup za rešavanje stohastičkih diferencijalnih jednačina koji se oslanja na teoriju belog šuma i haos ekspanzije. Kroz različite primere, zamenom običnog proizvoda Vikovim u jednačinama, prikazaćemo nove dokaze za stare rezultate, kao i postupak za određivanje eksplicitnih rešenja koja do sada nisu bila poznata, a koja pripadaju klasi uopštenih slučajnih procesa.

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