Dr. Peter Perczewski, Mannheim University
Date: 11 JUNE 2019 at 14:30
Event location: Room III, 2nd floor, Department of Statistics, Via Belle Arti 41, Bologna
Type: Statistics Seminars
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.