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SUMMARY:Estimation for SPDEs from noisy observations
DTSTART:20260320T151500
DTEND:20260320T161500
DTSTAMP:20260410T074507Z
UID:8942e4ee6927e9b8e070fe3137e03713f6d8f84616aaf31eaa960970
CATEGORIES:Conferences - Seminars
DESCRIPTION:Markus Reiss\, Humboldt-Universität zu Berlin\nWe consider s
 tochastic evolution equations of the form dX(t)=AθX(t)dt+BdWt\n\nwith a g
 enerator Aθ on a Hilbert space\, involving an unknown real or functional 
 parameter θ. We consider observations dY(t)=X(t)dt+εdVt\, t∈[0\,T]\, i
 n space-time white noise dV and ask about optimal estimation of θ. Minima
 x lower bounds reveal a rich picture\, which we shall describe in detail f
 or second-order elliptic operators Aθ=∇⋅(θ2∇+θ1)+θ0. Optimal rat
 es depend on the order of the coefficient θi\, the dimension and the asym
 ptotics taken. An even richer structure appears for nonparametric estimati
 on. The lower bound proofs rely on Hellinger bounds for cylindrical Gaussi
 an measures and functional calculus for non-commuting\, unbounded normal o
 perators. A rate-optimal parametric estimator is obtained by a subtle prea
 veraging approach. Finally\, a nonparametric diffusivity estimator and sev
 eral open problems are presented.\n\n\n 
LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517
STATUS:CONFIRMED
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