Discrete and Continuous Dynamical Systems - B · 2016 · 25 citations · 15 references
EngineeringMathematicsDynamical SystemsProbability TheoryStochastic ProcessesDiffusion ProcessesLévy ProcessesStochastic CalculusStochastic ControlStochastic Differential EquationsStochastic StabilityLipschitz ConditionsLévy-driven Stochastic Differential EquationsNumerical Methods For Stochastic Differential EquationsOrnstein - Uhlenbeck Processes Driven By Lévy NoiseStochastic IntegrationStochastic Partial Differential Equations
We extend the taming techniques developed in [3,19] to construct explicit Milstein schemes that numerically approximate Lévy driven stochastic differential equations with super-linearly growing drift coefficients. The classical rate of convergence is recovered when the first derivative of the drift coefficient satisfies a polynomial Lipschitz condition.
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Martin Hutzenthaler, Arnulf Jentzen, Peter E. Kloeden · The Annals of Applied Probability · 2012 · 439 citations · Full text
Engineering, Computational Engineering, Differential Equations +14
On stochastic equations with respect to semimartingales I.<sup>†</sup>
István Gyöngy · Stochastics · 1980 · 212 citations
A note on tamed Euler approximations
Sotirios Sabanis · Electronic Communications in Probability · 2013 · 191 citations · Full text