Georgia Institute of Technology College of Sciences

In this talk we shall discuss the problem of fitting a distribution function to the marginal distribution of a long memory process. It is observed that unlike in the i.i.d. set up, classical tests based on empirical process are relatively easy to implement. More importantly, we discuss fitting the marginal distribution of the error process in location, scale and linear regression models. An interesting observation is that the first order difference between the residual empirical process and the null model can not be used to asymptotically to distinguish between the two marginal distributions that differ only in their means. This finding is in sharp contrast to a recent claim of Chan and Ling to appear in the Ann. Statist. that such a process has a Gaussian weak limit. We shall also proposes some tests based on the second order difference in this case and analyze some of their properties. Another interesting finding is that residual empirical process tests in the scale problem are robust against not knowing the scale parameter. The third finding is that in linear regression models with a non-zero intercept parameter the first order difference between the empirical d.f. of residuals and the null d.f. can not be used to fit an error d.f. This talk is based on ongoing joint work with Donatas Surgailis.

We consider a stochastic Navier-Stokes equation driven by a space-time Wiener process. This equation is quantized by transformation of the nonlinear term to the Wick product form. An interesting feature of this type of perturbation is that it preserves the mean dynamics: the expectation of the solution of the quantized Navier-Stokes equation solves the underlying deterministic Navier-Stokes equation. From the stand point of a statistician it means that the perturbed model is an unbiased random perturbation of the deterministic Navier-Stokes equation.The quantized equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. A solution of the quantized version is unique if and only if the uniqueness property holds for the underlying deterministic Navier-Stokes equation. The generalized solution is obtained as an inverse of solutions to corresponding quantized equations. We will also demonstrate that it could be approximated by real (non-generalized processes). A solution of the quantized Navier-Stokes equation turns out to be nonanticipating and Markov. The talk is based on a joint work with R. Mikulevicius.

Research Horizons features Lunch Fun Break! The purpose is to create an opportunity for all graduate students, new and experienced, domestic and international, to meet, eat and have fun.AGENDA: ***"Suggestion box" for graduate students will be displayed in Faculty Lounge Skiles 236.*** Propective students' visit on Friday, April 2. *** Game: "Can you comunicate in silience?" *** PIZZAs, soft DRINKs, relax and have fun. ***