Tuesday, November 19, 2019 - 14:00 in V3-201
Drift estimation for linear SPDEs with fractional noise
A talk in the Bielefeld Stochastic Afternoon series by
Pavel Kříž from University of Chemistry and Technology, Prague
| Abstract: |
Two versions of minimum-contrast estimator of drift parameter in linear SPDEs with additive fractional noise will be introduced -- the energy version and the spectral version. The former is based on observation of energy of the solution and is studied in long-span asymptotic regime. Main tools inlcude ergodicity (for consistency) and the 4th moment techniques derived from Malliavin caclulus (for asymptotic normality and Berry-Esseen bounds). The latter version is tailored to observation of Fouriere modes of the solution and is studied in space-asymptotic regime (increasing number of modes). It utilizes self-similarity of fractional Brownian motion in combination with strong law of large numbers and the 4th moment theorem. Comparison to other types of estimators will be outlined. This is a joint work with Bohdan Maslowski.
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