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SUMMARY:Nonparametric Statistics for SPDEs - Markus Reiss (Humboldt Univer
 sity of Berlin)
DTSTART:20231110T140000Z
DTEND:20231110T150000Z
UID:TALK206017@talks.cam.ac.uk
CONTACT:Qingyuan Zhao
DESCRIPTION:Stochastic partial differential equations (SPDEs) are used mor
 e and more often to model real-world phenomena. Currently\, statistical me
 thodology for these equations driven by space-time white noise is developi
 ng rapidly. Based on the classical spectral method for parametric drift es
 timation\, we shall exhibit fundamental differences with the case of stoch
 astic ordinary differential equations. This method\, however\, is restrict
 ed to simple parametric situations and we discuss the local estimation met
 hod in detail\, which allows to estimate varying coefficients in the diffe
 rential operator of a parabolic SPDE nonparametrically with optimal rates.
  This approach is extended to observations under measurement errors ('stat
 ic noise')\, showing a fundamentally different impact of dynamic and stati
 c noise levels.  Finally\, we present an abstract minimax lower bound fram
 ework for stochastic evolution equations generated by normal operators in 
 Hilbert space and obtain a rich picture of complexity for different SPDE e
 stimation objectives. Some illustrations with cell motility experiments in
  biophysics are provided. 
LOCATION:MR12\, Centre for Mathematical Sciences
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