The Aziz Lectures were established by a generous gift from Prof. A. Kadir Aziz. The purpose of the lectures is to bring distinguished mathematicians to the University of Maryland, College Park, to give survey lectures on differential equations, their numerical analysis, and related areas.
Kadir Aziz, who died on March 25, 2016 at the age of 92, received his Ph.D. from the University of Maryland, College Park in 1957. He was on the faculty of Georgetown University from 1956 to 1967, and was on the faculty at the University of Maryland, Baltimore County (UMBC) since 1967. He was Professor Emeritus of Mathematics and Statistics at UMBC. Throughout his career Kadir Aziz was an active and highly respected member of the Numerical Analysis community at Maryland (The Aziz Lectures, n.d).
Smooth random functions and smooth random ODEs
September 12, 2018
Colloquium Room (MTH 3206)
Prof. Lloyd N. Trefethen
Abstract: What is a random function? What is noise? The standard answers are nonsmooth, defined pointwise via the Wiener process and Brownian motion. In the Chebfun project, we have found it more natural to work with smooth random functions defined by finite Fourier series with random coefficients. The length of the series is determined by a wavelength parameter lambda. Integrals give smooth random walks, which approach Brownian paths as lambda shrinks to 0, and smooth random ODEs, which approach stochastic DEs of the Stratonovich variety. Numerical explorations become very easy in this framework. There are plenty of conceptual challenges in this subject, starting with the fact that white noise has infinite amplitude and infinite energy, a paradox that goes back in two different ways to Einstein in 1905.
For more information, see www.math.umd.edu/aziz
University of Maryland. (n.d). The Aziz Lectures. Retrieved from https://www-math.umd.edu/research/aziz-lectures.