Step size control for the uniform approximation of systems of stochastic differential equations with additive noise.

DOI10.1214/aoap/1019487358zbMath1054.65007OpenAlexW2160546858MaRDI QIDQ1884833

Norbert Hofmann, Thomas Müller-Gronbach, Klaus Ritter

Publication date: 27 October 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1019487358

zbMATH Keywords

numerical exampleserror boundsasymptotic optimalitystep-size controladaptionsystems of stochastic differential equationspathwise approximation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Ordinary differential equations and systems with randomness (34F05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

The optimal uniform approximation of systems of stochastic differential equations ⋮ Complexity of stochastic integration in Sobolev classes ⋮ Complexity of Banach space valued and parametric stochastic Itô integration ⋮ Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations ⋮ The optimal free knot spline approximation of stochastic differential equations with additive noise ⋮ Strongly asymptotically optimal schemes for the strong approximation of stochastic differential equations with respect to the supremum error ⋮ Milstein scheme for stochastic differential equation with Markovian switching and Lévy noise ⋮ Convergence rate of strong local linearization schemes for stochastic differential equations with additive noise ⋮ Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients ⋮ High order local linearization methods: an approach for constructing A-stable explicit schemes for stochastic differential equations with additive noise ⋮ Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients ⋮ The optimal discretization of stochastic differential equations ⋮ Adaptive schemes for the numerical solution of SDEs -- a comparison ⋮ On the Moments of the Modulus of Continuity of Itô Processes ⋮ Loss of regularity for Kolmogorov equations

Cites Work

• Unnamed Item
• Unnamed Item
• Uniform reconstruction of Gaussian processes
• Step size control in the numerical solution of stochastic differential equations
• Approximation and optimization on the Wiener space
• An efficient approximation for stochastic differential equations on the partition ofsymmetricalirst
• Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design
• Variable Step Size Control in the Numerical Solution of Stochastic Differential Equations