2014Spring
Probability Seminar at University of Cincinnati
Spring 2014
Upcoming: Cincinnati Symposium on Probability Theory and Applications
September 19-21, 2014.
Jan 13, Mon, Yizao Wang
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: The maximum process of a Brownian motion with shot noise
Abstract: We introduce a new process as the maximum process of a Brownian motion, perturbed with shot noise. This new process naturally arises in the limit as the largest displacement of a random walk, with suitable perturbation.
The talk does not require any prerequisite. The proof is based on continuous mapping theorem. Background on weak convergence and continuous mapping theorem will be reviewed.
Joint work with Jacek Wesolowski.
Jan 20, Mon, MLK. No Seminar.
Jan 27, Mon, David Barrera
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: A Quenched Central Limit Theorem for Fourier Transforms of Ergodic Sequences.
Abstract: "Quenched" CLTs, or CLTs "started at a point", are currently a subject of intense research. When valid, they imply classical ("annealed") versions of CLTs, but they deal with asymptotic behavior under circumstances that annealed CLTs do not cover.
In this talk I will present a result recently submitted for publication stating a quenched CLT for Discrete Fourier Transforms (or "rotated" partial sums) of Ergodic Sequences. Necessary background will be provided and the essentials of the proof (which is a blend of Fourier Analysis, Operator Theory, and Martingale Approximation Techniques) will be explained.
Feb 3, Wlodek Bryc
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Integration with respect to q-Brownian motion.
Feb 10, Magda Peligrad
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Generalized Lindeberg's method
Abstract: The Lindeberg method helps to compare f[X(1),…,X(n)] with f[Y(1),…,Y(n)] for a smooth function f. Very often it is convenient take Y(1),…,Y(n) either independent random variables or a Gaussian vector. This method has many applications to Central Limit Theorem, random matrix theory, spin glasses and maxima of random fields.
Feb 17 Nages Shanmugalingam
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Dirichlet forms and heat kernels: Brownian motion from the analytic point of view
Feb 24, Florence Merlevède, Département de Mathématiques, Université de Marne-la-Vallée, France.
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Strong approximations in the dependent case.
Abstract: In this talk, I shall first present some recent results about strong approximation with rates for partial sums associated with a dependent stationary sequence of random variables. The conditions are expressed with the help of weakly dependent coefficients and will allow to get strong approximation results for the partial sums associated to non necessarily bounded iterates of some dynamical systems.
In the second part of the talk, I shall present strong approximations results with rates for the empirical process associated with a stationary sequence of random variables, either weakly dependent (univariate case), either absolutely regular (multlivariate case). The optimality of the results will also be discussed.
Mar 3, Stilian Stoev, University of Michigan, Ann Arbor
(Cancelled due to Winter Storm Titan)
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Tail behavior of Holder norms and limit theorems for maxima in Holder spaces
Abstract: We discuss some functional limit theorems of maxima in Holder spaces. It turns out that the classical tightness conditions of Lamperti readily apply, provided that one can control the tail-behavior of Holder norms of certain random processes. The powerful isomorphism theorem of Ciesielski allows one to obtain useful bounds on the tails of these Holder norms. Some implications on the path regularity of max-stable processes will be discussed.
Mar 13 (Thursday), Jack Silverstein, North Carolina State University
Room 135 Charlton, 4:35-5:30pm.
Title: Estimating population eigenvalues from large dimensional sample covariance matrices
Mar 17, Spring break. No Seminar.
Mar 21--23, AMS Sectional Meeting, Special Session on Stochastic Processes and Related Topics.
Mar 24, Jeesen Chen.
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: On some integration formulas
Mar 31, Magda Peligrad
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Universality for empirical spectral measure of a class of random matrices
Abstract: The talk will explain the use of multivariate Lindeberg's method to compare a function of a random fields with the same function of a Gaussian random field. The result is applied to prove the universality for empirical spectral measure.
April 7, Weiqing Yu
Seminar Room, French Hall 4206, 2:30-3:30pm
Title: Applying extreme value theory to risk evaluation
Abstract: Extreme value theory provides the mathematical foundation for risk evaluation and management, and it has been widely applied in finance, insurance, environmental sciences, hydrology, among others. In this capstone project, we review a few fundamental concepts and widely applied methodologies in extreme value theory. For practi- cal purpose, we develop an algorithm called adaptive grid algorithm, which is of independent interest for general optimization problem. We implement this algorithm to proceed maximum likelihood estimation for generalized extreme value distributions. Results are illustrated by simulations and a data analysis on the stock prices of Procter & Gamble.