Trees and asymptotic developments for fractional stochastic differential equations

Neuenkirch, Andreas ; Nourdin, Ivan ; Rößler, Andreas ; Tindel, Samy

Document Type: Working paper
Year of publication: 2018
Place of publication: Ithaca, NY
Publishing house: Cornell University
Edition: Version July 5, 2018
Publication language: English
Institution: School of Business Informatics and Mathematics > Wirtschaftsmathematik II: Stochastische Numerik (Neuenkirch 2013-)
Subject: 510 Mathematics
Abstract: In this paper we consider a n-dimensional stochastic differential equation driven by a fractional Brownian motion with Hurst parameter H>1/3. After solving this equation in a rather elementary way, following the approach of Gubinelli, we show how to obtain an expansion for E[f(X\_t)] in terms of t, where X denotes the solution to the SDE and f:R^n->R is a regular function. With respect to the work by Baudoin and Coutin, where the same kind of problem is considered, we try an improvement in three different directions: we are able to take a drift into account in the equation, we parametrize our expansion with trees (which makes it easier to use), and we obtain a sharp control of the remainder.

Dieser Eintrag ist Teil der Universitätsbibliographie.

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