Wednesday, April 20, 2005
| Topic |
Toeplitz matrices, Part III |
| Speaker |
Ed Cureg |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Wednesday, April 13, 2005
| Topic |
An Application of Curtiss' Continuity Theorem to Random Integer Partitions |
| Speaker |
Lyuben Mutafchiev |
| Time |
4:30-5:30 p.m. |
| Place |
PHY 013 |
Wednesday, April 6, 2005
| Time |
4:00-5:00 p.m. |
| Speaker |
Dmitri Prokhorov |
| Place |
PHY 013 |
Wednesday, March 30, 2005
| Topic |
Cybenko's results on approximation by superpositions of a sigmoidal function |
| Speaker |
Dmitri Prokhorov |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Wednesday, March 23, 2005
| Topic |
TBA |
| Speaker |
Norbert Youmbi |
| 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.)
Wednesday, March 9, 2005
| Topic |
Levy continuity theorem on moment generating functions |
| Speaker |
A. Mukherjea |
| 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 mgfs 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.
Wednesday, March 2, 2005
| Topic |
Weak Limits |
| Speaker |
Professor M. Rao
Department of Mathematics
University of Florida |
| 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.
Wednesday, February 16, 2005
| Topic |
Toeplitz matrices, Part II |
| Speaker |
Ed Cureg |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Abstract
We will establish asymptotic equivalence between Toeplitz and circulant matrices.
Wednesday, February 9, 2005
| Topic |
Toeplitz matrices |
| Speaker |
Ed Cureg |
| 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.
Wednesday, February 2, 2005
| Topic |
Identification of the parameters by knowing the minimum, Part III |
| Speaker |
John C. Davis, III |
| Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Wednesday, January 26, 2005
| Topic |
Multivariate Analysis, Part II |
| Speaker |
John C. Davis, III |
Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Abstract
Let \(X\) be an \(n\)-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.
Wednesday, January 19, 2005
| Topic |
Multivariate Analysis, Part I |
| Speaker |
Professor Arunava Mukherjea |
Time |
4:00-5:00 p.m. |
| Place |
PHY 013 |
Abstract
TBA.