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CATEGORIES:Probability
SUMMARY:A polynomial expansion for Brownian motion and the
  associated fluctuation process - Karen Habermann 
 (Warwick)
DTSTART;TZID=Europe/London:20220905T150000
DTEND;TZID=Europe/London:20220905T160000
UID:TALK178460AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/178460
DESCRIPTION:We start by deriving a polynomial expansion for Br
 ownian motion expressed in terms of shifted Legend
 re polynomials by considering Brownian motion cond
 itioned to have vanishing iterated time integrals 
 of all orders. We further discuss the fluctuations
  for this expansion and show that they converge in
  finite dimensional distributions to a collection 
 of independent zero-mean Gaussian random variables
  whose variances follow a scaled semicircle. We th
 en link the asymptotic convergence rates of approx
 imations for Brownian L\\'evy area which are based
  on the Fourier series expansion and the polynomia
 l expansion of the Brownian bridge to these limit 
 fluctuations. We close with a general study of the
  asymptotic error arising when approximating the G
 reen's function of a Sturm-Liouville problem throu
 gh a truncation of its eigenfunction expansion\, b
 oth for the Green's function of a regular Sturm-Li
 ouville problem and for the Green's function assoc
 iated with the classical orthogonal polynomials.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Jason Miller
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