We analyze the pathwise approximation for systems of stochastic
differential equations.The pathwise distance between the solution and its
approximation is measured globally on the unit interval in the
$L_{\infty}$-norm, and we study the expectation of this distance. For systems
with additive noise we obtain sharp lower and upper bounds for the minimal
error in the class of arbitrary methods which use discrete observations of a
Brownian path. The optimal order is achieved by an Euler scheme with adaptive
step-size control. We illustrate the superiority of the adaptive method
compared to equidistant discretization by a simulation experiment.
Publié le : 2000-05-14
Classification:
Systems of stochastic differential equations,
pathwise approximation,
adaption,
step-size control,
asymptotic optimality,
65U05,
60H10
@article{1019487358,
author = {Hofmann, Norbert and M\"uller-Gronbach, Thomas and Ritter, Klaus},
title = {Step size control for the uniform approximation of systems of
stochastic differential equations with additive noise},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 616-633},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487358}
}
Hofmann, Norbert; Müller-Gronbach, Thomas; Ritter, Klaus. Step size control for the uniform approximation of systems of
stochastic differential equations with additive noise. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 616-633. http://gdmltest.u-ga.fr/item/1019487358/