We analyze numerical methods for the pathwise
approximation of a system of stochastic differential equations. As
a measure of performance we consider the $q$th mean of the maximum
distance between the solution and its approximation on the whole
unit interval. We introduce an adaptive discretization that takes
into account the local smoothness of every trajectory of the
solution. The resulting adaptive Euler approximation performs
asymptotically optimal in the class of all numerical methods that
are based on a finite number of observations of the driving
Brownian motion.
Publié le : 2002-05-14
Classification:
Systems of stochastic differential equations,
pathwise uniform approximation,
asymptotic optimality,
adaptive method,
65U05,
60H10
@article{1026915620,
author = {M\"uller-Gronbach, Thomas},
title = {The optimal uniform approximation of systems of stochastic differential equations},
journal = {Ann. Appl. Probab.},
volume = {12},
number = {1},
year = {2002},
pages = { 664-690},
language = {en},
url = {http://dml.mathdoc.fr/item/1026915620}
}
Müller-Gronbach, Thomas. The optimal uniform approximation of systems of stochastic differential equations. Ann. Appl. Probab., Tome 12 (2002) no. 1, pp. 664-690. http://gdmltest.u-ga.fr/item/1026915620/