LMS Journal of Computation and Mathematics · 2003 · 102 citations · 11 references
Natural SciencesMathematicsDifferential EquationsStochastic ModelingStochastic ProcessesComputational MathematicsNumerical ConvergenceNumerical Methods For Differential EquationsNumerical StabilityStochastic CalculusStochastic Differential EquationsLipschitz ConditionsLipschitz ContinuityMean Square ConvergenceNumerical Methods For Stochastic Differential EquationsUniqueness For Functional Differential EquationsUniqueness Theorems
Abstract In this paper, the strong mean square convergence theory is established for the numerical solutions of stochastic functional differential equations (SFDEs) under the local Lipschitz condition and the linear growth condition. These two conditions are generally imposed to guarantee the existence and uniqueness of the true solution, so the numerical results given here were obtained under quite general conditions.
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Stochastic differential equations and applications
Gian‐Carlo Rota · Advances in Mathematics · 1977 · 1.2K citations