STOCHASTICS WITH APPLICATIONS Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice seminara Stohastika sa primenama:
https://miteam.mi.sanu.ac.rs/asset/n4AMxqgneB2qxFuT2

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Plan rada seminara Stohastika sa primenama za APRIL 2025.

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Četvrtak, 10.04.2025. u 18:00, Online
Persi Diaconis, Stanford University
THE MATHEMATICS OF SOLITAIRE
One of the embarrassments of my subject (probability and combinatorics) is that we can't figure out the odds of winning at solitaire. People play solitaire, millions of times a day. I mean the usual Klondike solitaire with seven piles of cards on everyone's phones and computers. What's the chance of winning? How can I play well? As usual, 'when there is a hard problem you can't solve, there is an easier problem you can't solve'. I'll introduce an easier variant, 'Patience Sorting', which looks similar and permits analysis. This analysis isn't so easy and the need some of the deepest tools we have exactly solvable models and the Tracy Widom distribution. The results illuminate the distance between parked cars, the shape of a burning piece of paper and the circles left by coffee cups. ll also tell what is known about 'real solitaire’.

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Četvrtak, 24.04.2025. u 11:00, Online
Ljiljana Petrović, University of Belgrade
MARKOVIAN EXTENSIONS OF A STOCHASTIC PROCESS IN CONTINUOUS TIME
In many forecasting or optional control problems stochastic models are appropriate and Markov processes are the most often used models in such cases. So, it is of interest to find markovian representations of a given stochastic process.
In many problems it is natural to consider minimal markovian extensions. We consider a problem (that follows directly from realization problem): find all minimal markovian extensions for a given stochastic process. More precisely, we analyze the problem on existence of a minimal Markovian (in the wide sense) process which contains a given stochastic process as a component.
We will work with families of Hilbert spaces and with families of $\sigma$-algebras generated by given stochastic processes.

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