﻿ MISANU
ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Seminar on Stohastics

PROGRAM

SEMINAR IZ STOHASTIKE
Matematicki institut SANU
Kneza Mihaila 35/1

PLAN RADA SEMINARA ZA NOVEMBAR 2005.

Cetvrtak, 10. novembar u 12 h.
12h Katica (Stevanovic) Hedrih:

Transversal Vibration of a Parametrically Excited Hereditary Beam: Stochastic Stability of Deformable Forms and Processes

The partial differential equation of transversal stochastic vibration of a parametrically excited hereditary beam was derived. The beam is graded by an hereditary material with known relaxation kernel, and it is subject to axial stochastic external excitation. The influence of rotatory inertia of beam cross section and transverse shear of beam cross section under the transverse force, and the corresponding members in the partial differential equation are taken into account. Bernoulli particular integral method and Lagrange method of variation constant are used for the transformation problem. The asymptotic averaged method is used for obtaining the first approximation of Ito stochastic differential equations. The sets of Lyapunov exponents are obtained.

13h Slobodanka Jankovic:

Ravnomerna raspodela i stabilnost jedne njene karakterizacije

Neka je $(\Omega ,F,P)$ prostor verovatnoce i neka je $X$ slucajna promenljiva koja uzima vrednosti u separabilnom metrickom prostoru $S$. Sa $\rho$ je oznacena metrika definisana na $S$, a sa $\mu$ verovatnosna mera ravnomerne raspodele na $S$, koja dodeljuje jednaku verovatnocu svim zatvorenim kuglama jednakog poluprecnika. Naime, ako je $r\ge 0$ i $B(x,r)=\{y:\rho (x,y)\le r\}$, tada je $\mu _{r}=\mu (B(x,r))$ jednako za svako $x\in S$. U ovim okvirima bice dokazana stabilnost karakterizacije ravnomerne raspodele, koja je bazirana na nezavisnosti nekih slucajnih promenljivih.

Cetvrtak, 24. novembar u 12 h.
12h Slobodanka S. Mitrovic:

Stochastic modeling of the number of felled trees in selection stands

The problem of forecasting the number of trees in the selection stands predicted for harvesting in a future period, so that the main resource of the number of trees is sustained. This is achieved by stochastic modeling of the number of felled trees and by solving the certain partial differential equation.

13h Milan Merkle:

Visedimenzionalne medijane i centar raspodele

U statistici je poznato nekoliko razlicitih (i ne-ekvivalentnih) generalizacija pojma medijane na visedimenzionalni skup podataka ili raspodelu. U svim tim generalizacijama polazi se od jedne od ekvivalentnih karakterizacija medijane za slucajnu promenljivu, i onda se takva karakterizacija prenosi na vise dimenzija. Medjutim, osobine koje su ekvivalentne u jednoj dimenziji, nisu ekvivalentne u vise dimenzija, tako da definitivno zadovoljavajuce resenje definisanja visedimenzionalne medijane (ili tzv. centra raspodele) nije nadjeno. Ovde ce biti predstavljen jos jedan pristup definisanju centra raspodele, kao i nekoliko interesantnih rezultata u vezi s tim.

Slobodanka Jankovic i Svetlana Jankovic
rukovodioci seminara

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