Mathematical Colloquium
PROGRAM
ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU
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PROGRAM ZA OKTOBAR 2017.
PONEDELJAK, 02.10.2017. u 15:15, Sala 301f, MI SANU, Kneza Mihaila 36
Hermann Thorisson, Department of Mathematics, University of Iceland
COUPLING METHODS IN PROBABILITY THEORY
Coupling means the joint construction of two or more random variables, processes, or any random objects. The aim of the construction is often to deduce properties of the individual objects or to gain insight into distributional relations between them.
In this talk we shall first consider some elementary examples, moving from Poisson approximation and stochastic domination to Markov chains and Brownian motion. We then briefly outline a general coupling theory for stochastic processes and finally extend the view to random elements under a topological transformation group.
ČETVRTAK, 26.10.2017. u 15:15, Sala 301f, MI SANU, Kneza Mihaila 36
Waclaw Boleslaw Marzantowicz, University of Poznan, Poland
BOURGIN-YANG THEOREM AS A FINE VERSION OF THE BORSUK-ULAM THEOREM
Teorema Borsuka-Ulama spada među najpoznatije topološke rezultate koji imaju veliki broj primena i van topologije. Teorema Burgina-Janga (Bourgin-Yang) predstavlja jedno "kvantitativno uopštenje" teoreme Borsuka-Ulama koje je otvorilo put novim kohomološkim tehnikama u ovoj oblasti. Predavanje je pregled rezultata i primena metoda ekvivarijatne topologije (u kombinatorici, nelinearnoj analizi i geometriji) od početaka do novijih istraživanja u ovoj oblasti, uključujući i najnovije rezultate predavača i njegovih saradnika (D. de Mattos, E. dos Santos, i dr.).
PETAK, 27.10.2017. u 14:15, Sala 301f, MI SANU, Kneza Mihaila 36
Jordan Stoyanov, Bulgarian Academy of Sciences, Sofia, Bulgaria; Newcastle University, United Kingdom
MOMENT DETERMINACY OF PROBABILITY DISTRIBUTIONS
We deal with distributions (or measures), one-dimensional or multi-dimensional, with finite all moments. It is well-known that any such a distribution is either uniquely determined by its moment (M-determinate) or it is non-unique (M-indeterminate). This is the classical moment problem originated in works by Chebyshev, Markov and Stieltjes. Well-known are general conditions which are "iff", but they cannot be checked. Thus our discussion will be on easier and checkable conditions for either uniqueness or non-uniqueness applied to probability distributions.
The emphasis will be on some recent developments such as:
- Krein's condition. Converse Krein's condition and Lin's condition.
- Stieltjes classes for M-indeterminate distributions. Index of dissimilarity.
- Hardy's condition. Multidimensional moment problem.
- Rate of growth of the moments for (in)determinacy.
There will be results, some of them very new, hints for their proof, examples and counterexamples, and also open questions.
Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.
Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU
