The Optimal Discretization of Stochastic Differential Equations
Copyright policy )The Optimal Discretization of Stochastic Differential Equations
The paper studies discrete time pathwise approximations of stochastic differential equations. An adaptive discretization is introduced that reflects local properties of the simulated trajectory. The corresponding error is shown to converge to zero in average with a certain rate. The method allows the determination of the complexity of pathwise approximations.
- Technische Universität Darmstradt Germany
- TU Darmstadt Germany
- Goethe University Frankfurt Germany
- TECHNISCHE UNIVERSITAT DARMSTADT Germany
- Johann Wolfgang Goethe-Universitaet Germany
Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Applied Mathematics, stochastic differential equation, Stochastic ordinary differential equations (aspects of stochastic analysis), Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, lower bounds, pathwise approximation, strong approximation, asymptotic optimality, adaptive scheme, complexity, adaptive discretization
Statistics and Probability, Numerical Analysis, Algebra and Number Theory, Control and Optimization, Applied Mathematics, stochastic differential equation, Stochastic ordinary differential equations (aspects of stochastic analysis), Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations, lower bounds, pathwise approximation, strong approximation, asymptotic optimality, adaptive scheme, complexity, adaptive discretization
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