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An adaptive discretization algorithm for the weak approximation of stochastic differential equations
Author(s) -
Rößler Andreas
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410005
Subject(s) - discretization , stochastic differential equation , bounded function , mathematics , stochastic partial differential equation , differential equation , discretization error , algorithm , mathematical optimization , computer science , mathematical analysis
Numerical methods with fixed step size have limitations if they are applied for example to stiff stochastic differential equations where the step size is forced to be very small. In this paper, an adaptive step size control algorithm for the weak approximation of stochastic differential equations is introduced. The proposed algorithm calculates an estimation of the local error in order to determine the optimal step size such that the local error is bounded by some given tolerances. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)