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arXiv · 0908.1021

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

Hideyuki Tanaka·Arturo Kohatsu-Higa
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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 Lévy driven stochastic differential equations.

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Hideyuki Tanaka, Arturo Kohatsu-Higa. 2009-08-07. An operator approach for Markov chain weak approximations with an application to infinite activity Lévy driven SDEs. https://doi.org/10.1214/08-aap568

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