An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs

Details An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs

2009-08-07

arxiv.org/abs/0908.1021v1

Annals of Applied Probability 2009, Vol. 19, No. 3, 1026-1062

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-AAP568 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/08-AAP568

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.

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