Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 43, Issue 3, Pages 1139-1154Publisher
SIAM PUBLICATIONS
DOI: 10.1137/040612026
Keywords
SDEs with nonglobally Lipschitz coefficients; numerical integration of SDEs in the weak sense
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We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently large sphere. We prove that accuracy of any method of weak order p is estimated by epsilon + O(h(p)), where epsilon can be made arbitrarily small with increasing radius of the sphere. The results obtained are supported by numerical experiments.
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