Statistics seminar 2019 - “Optimal approximation of (anticipating) SDEs"

  • Data: 11 giugno 2019 dalle 14:30 alle 16:30

  • Luogo: Dipartimento di Scienze Statistiche - via delle Belle Arti 41 - Aula III - 2° piano

Peter Perczewski - Mannheim University

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.

Alberto Lanconelli

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