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CATEGORIES:Seminar
DESCRIPTION:What is a random function? What is noise? The standard answer
s are nonsmooth\, defined pointwise via the Wiener process and Brownian mot
ion. In the Chebfun project\, we have found it more natural to work with s
mooth random functions defined by finite Fourier series with random coeffic
ients. The length of the series is determined by a wavelength parameter $\
lambda$. Integrals give smooth random walks\, which approach Brownian paths
as $\lambda\to 0$\, and smooth random ODEs\, which approach stochastic DEs
of the Stratonovich variety. Numerical explorations become very easy in t
his framework. There are plenty of conceptual challenges in this subject\,
starting with the fact that white noise has infinite amplitude and infinit
e energy\, a paradox that goes back two different ways to Einstein in 1905.
\n\n\nBio:\nNick Trefethen is Professor of Numerical Analysis and head of t
he Numerical Analysis Group at Oxford University. He was educated at Harva
rd and Stanford and held positions at NYU\, MIT\, and Cornell before moving
to Oxford in 1997. He is a Fellow of the Royal Society and a member of th
e US National Academy of Engineering\, and served during 2011-2012 as Presi
dent of SIAM. As an author Trefethen is known for his books including Numer
ical Linear Algebra (1997)\, Spectral Methods in MATLAB (2000)\, Spectra an
d Pseudospectra (2005)\, Approximation Theory and Approximation Practice (2
013)\, and Exploring ODEs (to appear in 2018). He organized the SIAM 100-D
ollar\, 100-Digit Challenge in 2002 and is the inventor of Chebfun.
DTEND:20170901T203000Z
DTSTAMP:20171217T030843
DTSTART:20170901T193000Z
GEO:42.443451;-76.481506
LOCATION:Frank H. T. Rhodes Hall\, 655
SEQUENCE:0
SUMMARY:CAM Colloquium: Nick Trefethen (Oxford University) - Random Functi
ons\, Random Odes\, and Chebfun
UID:tag:localist.com\,2008:EventInstance_2965672
URL:http://events.cornell.edu/event/cam_colloquium_nick_trefethen_oxford_un
iversity_-_random_functions_random_odes_and_chebfun
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