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Explicit Order 1.5 Schemes for the Strong Approximation of Itô Stochastic Differential Equations
Author(s) -
Rößler Andreas
Publication year - 2005
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200510380
Subject(s) - stochastic differential equation , mathematics , order (exchange) , class (philosophy) , stochastic partial differential equation , differential equation , differential (mechanical device) , mathematical analysis , computer science , physics , economics , thermodynamics , finance , artificial intelligence
A new class of stochastic Runge‐Kutta (SRK) methods for the strong approximation of It ô stochastic differential equation systems w.r.t. an one‐dimensionalWiener process is introduced. Some coefficients for a SRK method converging at least with order 1.5 in the strong sense are presented. Further, a special SRK scheme having deterministic order 4.0 is proposed for stochastic differential equations with small noise. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)