Statistics Seminars 2019

Martedì 11 Giugno 2019 ore 14,30 

Aula III, secondo piano, Dipartimento di Scienze Statistiche

"Optimal approximation of (anticipating) SDEs"

Dott. Peter Parczewski, Mannheim University

Abstract 
We present a general mean squared error expansion for 
optimal  approximation of Wiener functionals based on finite and 
equidistant observations of the Brownian motion.The expansion is 
given in terms of Malliavin calculus and the terms involved exhibit  
Hilbert space structures. This gives lower error bounds for arbitrary 
numerical schemes which are constructed from an equidistant information 
of the Brownian motion. Due to this expansion we are able to recover
 and improve many results on optimal approximation of Ito SDEs and 
anticipating SDEs, where the integral is interpreted in Skorohod sense, a
 mean zero extension of the Ito integral to nonadapted integrands.

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Alberto Lanconelli
Dipartimento di Scienze Statistiche "Paolo Fortunati"
Alma Mater Studiorum - Università di Bologna