Colloquia — Summer 2005
Friday, May 27, 2005
| Title |
Statistical inference for branching processes |
| Speaker |
Professor Nikolay Yanev
Department of Probability and Statistics
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences
Sofia, Bulgaria |
| Time |
10:00-11:00 a.m. |
| Place |
PHY 109 |
| Sponsor |
Professor George Yanev |
Abstract
It is well known that branching processes have a lot of
applications, in particular in biology and medicine. We will discuss the
asymptotic behavior of branching populations having an increasing
random number of ancestors. We will present an estimation theory
for the mean, variance, and offspring distributions of the
processes Zt(n) with a random number
of ancestors
Z0(n), as both n (and thus Z0(n)
in some sense) and t ∞. Non-parametric, consistent, and
asymptotically normal estimators will be proposed. Some censored
estimators will also be considered. We will show that all results
can be transferred to branching processes with immigration, under
an appropriate sampling scheme. A software system for simulation
and estimation of branching processes will be demonstrated.
Friday, May 20, 2005
| Title |
Variational comparison method and qualitative analysis of time series |
| Speaker |
Professor G. S. Ladde
Department of Mathematics
The University of Texas at Arlington |
| Time |
10:00-11:00 a.m. |
| Place |
PHY 109 |
| Sponsor |
Professor C. Tsokos |
Abstract
In this work, the study of convergence and stability analysis of stochastic
iterative processes under both structural perturbations is outlined. The random
structural perturbations are described by a Markov chain with a finite number
of states. Under algebraic conditions on rate functions and an intensity matrix
associated with the Markov chain, convergence and stability results are obtained.
This is achieved through the development and the introduction of variational
comparison theorems in the context of a Lyapunov-like function. Furthermore,
hereditary effects and the effects of random structural perturbations are analyzed.
The mathematical conditions are algebraically simple, easy to verify, and robust
to the parametric changes in the system. Several examples are given to illustrate
the usefulness of the technique.