The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.
Numerical methods for stoc hastic delay differential equations via the Wong-Zakai approximation
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Develops strong mean-square approximations for iterated stochastic integrals of multiplicity k using generalized multiple Fourier series expansions, with explicit error formulas and applications to numerical solution of Ito SDEs and semilinear SPDEs.
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Implementation of Milstein Schemes for Stochastic Delay-Differential Equations with Arbitrary Fixed Delays
The authors give practical implementations of order-1/2 and order-1 strong schemes for SDDEs with arbitrary fixed delays by combining linear interpolation on a fixed mesh and an augmented variable-step mesh that includes all required delay points.
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Strong Approximation of Iterated Ito and Stratonovich Stochastic Integrals Based on Generalized Multiple Fourier Series. Application to Numerical Solution of Ito SDEs and Semilinear SPDEs
Develops strong mean-square approximations for iterated stochastic integrals of multiplicity k using generalized multiple Fourier series expansions, with explicit error formulas and applications to numerical solution of Ito SDEs and semilinear SPDEs.