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Milstein-type semi-implicit split-step numerical methods for nonlinear SDE with locally Lipschitz drift terms

ABSTRACT
We develop Milstein-type versions of semi-implicit split-step methods for numerical solutions of nonlinear stochastic differential equations (SDE) with locally Lipschitz coefficients. Under a one-sided linear growth condition on the drift term, we obtain some moment estimates and discuss convergence properties of these numerical methods. We compare the performance of multiple methods, including the backward Milstein, tamed Milstein and truncated Milstein procedures on nonlinear SDE including generalized stochastic Ginzburg-Landau equations. In particular, we discuss their empirical rates of convergence.
KEYWORDS
PAPER SUBMITTED: 2018-09-12
PAPER REVISED: 2018-10-01
PAPER ACCEPTED: 2018-10-26
PUBLISHED ONLINE: 2018-12-16
DOI REFERENCE: https://doi.org/10.2298/TSCI180912325I
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