| Speaker | Ed Cureg |
| Topic | Toeplitz matrices, Part III |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
| Speaker | Lyuben Mutafchiev |
| Topic | An Application of Curtiss' Continuity Theorem to Random Integer Partitions |
| Time | 4:30-5:30 p.m. |
| Place | PHY 013 |
| Speaker | Dmitri Prokhorov |
| Topic | Cybenko's results on approximation by superpositions of a sigmoidal function, Part II |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
| Speaker | Dmitri Prokhorov |
| Topic | Cybenko's results on approximation by superpositions of a sigmoidal function |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
| Speaker | Norbert Youmbi |
| Topic | TBA |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
The statement XY and Y have the same distribution, where X and Y are two independent S-valued random variables, is well-understood when S is a (multiplicative) group. An equivalent problem is one of studying the Choquet convolution equation P * Q = Q for probability measures P and Q. We'll consider this question when S is a hypergroup. (Concepts such as hypergroups and convolutions in hypergroups will be introduced first.)
| Speaker | A. Mukherjea |
| Topic | Levy continuity theorem on moment generating functions |
| Time | 4:30-5:30 p.m. |
| Place | PHY 013 |
Abstract
Many graduate probability texts contain this theorem. The most general version
(see J. H. Curtiss, Ann. Math. Stat.,1942)
available in printed form is: If a sequence of mgf s converges in an
interval CONTAINING 0, then it must converge uniformly in every
closed subinterval of that interval, and the limit function must,
itself, be a mgf. Furthermore, the corresponding sequence of distribution functions
must converge weakly to the distribution function that corresponds to the limiting
mgf.
| Speaker | Professor M. Rao Department of Mathematics University of Florida |
| Topic | Weak Limits |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
Weak convergence of measures is a concept of great importance in Probability Theory. The Central Limit Theorem is just one example. In this preliminary note, we will discuss weak convergence of measures with "boundary" conditions.
| Speaker | Ed Cureg |
| Topic | Toeplitz matrices, Part II |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
We will establish asymptotic equivalence between Toeplitz and circulant matrices.
| Speaker | Ed Cureg |
| Topic | Toeplitz matrices |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
Examples of such matrices are covariance matrices of weakly
stationary stochastic time series. The aim of the talk is
to relate these matrices to their simpler, more structured
cousin - the circulant matrices.
| Speaker | John C. Davis, III |
| Topic | Identification of the parameters by knowing the minimum, Part III |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
| Speaker | John C. Davis, III |
| Topic | Multivariate Analysis, Part II |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
Let X be a n-variate non-singular normal vector whose parameters are not known. However, the pdf of Y, the minimum of the entries of X, is known. Is it then possible to identify the parameters knowing only this pdf? This general problem, though relevant in numerous practical contexts, has remained unsolved for many years. A special case, when all the correlations are negative, will be discussed.
For practical examples, think of (Supply, Demand) as an unknown bivariate normal, where you actually observe the minimum, the actual amount passing from the sellers to the buyers. You can also think of a machine with multiple parts where the survival times of the parts is a unknown multivariate normal; in case this machine fails as soon as one of its parts fails, then again you know only the minimum of the survival times.
| Speaker | Professor Arunava Mukherjea |
| Topic | Multivariate Analysis, Part I |
| Time | 4:00-5:00 p.m. |
| Place | PHY 013 |
Abstract
TBA.
Please direct questions to mthmaster@nosferatu.cas.usf.edu.
Last updated: 2005-04-20.
Copyright © 2000, USF Department of Mathematics.