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VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20221019T124026Z
DTSTART:20221109T150000Z
DTEND:20221109T160000Z
SUMMARY:Randolf Altmeyer - Optimal parameter estimation for linear SPDEs
from multiple local measurements (in-person)
UID:{http://www.columbasystems.com/customers/uom/gpp/eventid/}xir-l9fmcbm
5-cy0ibd
DESCRIPTION:Randolf Altmeyer (University of Cambridge) will speak in the
Probability seminar. \n\nThe problem of parameter estimation in a genera
l second order linear stochastic partial differential equation (SPDE) is
considered. One trajectory of the solution to the SPDE is observed cont
inuously in time and averaged in space over a small window at multiple l
ocations. Estimators for the diffusivity\, transport and reaction coeffi
cients are constructed. These estimators are shown to be minimax rate op
timal by proving an explicit lower bound in the asymptotic regime where
the spatial window shrinks to zero and with a growing number of observat
ions. Interestingly\, the rate of convergence depends on the differentia
l order in which the respective coefficient appears\, with the fastest r
ate achieved for the diffusivity coefficient and the slowest rate for th
e reaction terms. The proof for the lower bounds relies on an explicit a
nalysis of the reproducing kernel Hilbert spaces for the observed Gaussi
an processes\, which we derive here\, and may be of independent interest
.
STATUS:TENTATIVE
TRANSP:TRANSPARENT
CLASS:PUBLIC
LOCATION:Frank Adams Room 2\, Alan Turing Building\, Manchester
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