Approximating the signature of Brownian motion for high order SDE simulation

Autor:	Foster, James
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Mathematics - Probability 60H35 60J65 60L90 65C30
Druh dokumentu:	Working Paper
Popis:	The signature is a collection of iterated integrals describing the "shape" of a path. It appears naturally in the Taylor expansions of controlled differential equations and, as a consequence, is arguably the central object within rough path theory. In this paper, we will consider the signature of Brownian motion with time, and present both new and recently developed approximations for some of its integrals. Since these integrals (or equivalent L\'{e}vy areas) are nonlinear functions of the Brownian path, they are not Gaussian and known to be challenging to simulate. To conclude the paper, we will present some applications of these approximations to the high order numerical simulation of stochastic differential equations (SDEs). Comment: 69 pages, 12 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.10118 Zobrazit plný text záznamu View this record from Arxiv