Convergence Rates for Approximations of Functionals of SDEs
Avikainen, Rainer
arXiv, 0712.3635 / Harvested from arXiv
Text on arXiv
We consider upper bounds for the approximation error E|g(X)-g(\hat X)|^p, where X and \hat X are random variables such that \hat X is an approximation of X in the L_p-norm, and the function g belongs to certain function classes, which contain e.g. functions of bounded variation. We apply the results to the approximations of a solution of a stochastic differential equation at time T by the Euler and Milstein schemes. For the Euler scheme we provide also a lower bound.
Publié le : 2007-12-21
Classification:  Mathematics - Probability,  60H10, 41A25, 26A45, 65C20, 65C30 
@article{0712.3635,
     author = {Avikainen, Rainer},
     title = {Convergence Rates for Approximations of Functionals of SDEs},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0712.3635}
}

Avikainen, Rainer. Convergence Rates for Approximations of Functionals of SDEs. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0712.3635/