In this article we develop a new methodology to prove weak approximation results for general stochastic differential equations. Instead of using a partial differential equation approach as is usually done for diffusions, the approach considered here uses the properties of the linear equation satisfied by the error process. This methodology seems to apply to a large class of processes and we present as an example the weak approximation of stochastic delay equations.
@article{1159804977,
author = {Cl\'ement, Emmanuelle and Kohatsu-Higa, Arturo and Lamberton, Damien},
title = {A duality approach for the weak approximation of stochastic differential equations},
journal = {Ann. Appl. Probab.},
volume = {16},
number = {1},
year = {2006},
pages = { 1124-1154},
language = {en},
url = {http://dml.mathdoc.fr/item/1159804977}
}
Clément, Emmanuelle; Kohatsu-Higa, Arturo; Lamberton, Damien. A duality approach for the weak approximation of stochastic differential equations. Ann. Appl. Probab., Tome 16 (2006) no. 1, pp. 1124-1154. http://gdmltest.u-ga.fr/item/1159804977/