An operator approach for Markov chain weak approximations with an application to infinite activity L\'{e}vy driven SDEs
Probability
2009-08-10 v1
Abstract
Weak approximations have been developed to calculate the expectation value of functionals of stochastic differential equations, and various numerical discretization schemes (Euler, Milshtein) have been studied by many authors. We present a general framework based on semigroup expansions for the construction of higher-order discretization schemes and analyze its rate of convergence. We also apply it to approximate general L\'{e}vy driven stochastic differential equations.
Keywords
Cite
@article{arxiv.0908.1021,
title = {An operator approach for Markov chain weak approximations with an application to infinite activity L\'{e}vy driven SDEs},
author = {Hideyuki Tanaka and Arturo Kohatsu-Higa},
journal= {arXiv preprint arXiv:0908.1021},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/08-AAP568 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)