Strongly asymptotically optimal schemes for the strong approximation of stochastic differential equations with respect to the supremum error
DOI10.1016/j.jco.2020.101496zbMath1469.65030arXiv1901.06148OpenAlexW3100661459WikidataQ115350162 ScholiaQ115350162MaRDI QIDQ2192675
Publication date: 17 August 2020
Published in: Journal of Complexity (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1901.06148
stochastic differential equationsstrong approximationasymptotic lower error boundsasymptotic upper error boundsstrong asymptotic optimalitytamed Euler schemes
Numerical methods (including Monte Carlo methods) (91G60) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)
Cites Work
- Unnamed Item
- Euler approximations with varying coefficients: the case of superlinearly growing diffusion coefficients
- On stochastic differential equations with arbitrary slow convergence rates for strong approximation
- Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
- Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
- The truncated Euler-Maruyama method for stochastic differential equations
- Strong rate of tamed Euler-Maruyama approximation for stochastic differential equations with Hölder continuous diffusion coefficient
- Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients
- Higher-order implicit strong numerical schemes for stochastic differential equations
- On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients
- Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
- Adaptive Euler-Maruyama method for SDEs with non-globally Lipschitz drift
- The truncated Milstein method for stochastic differential equations with commutative noise
- The optimal uniform approximation of systems of stochastic differential equations
- Step size control for the uniform approximation of systems of stochastic differential equations with additive noise.
- On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients
- On the performance of the Euler-Maruyama scheme for SDEs with discontinuous drift coefficient
- Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
- On non-polynomial lower error bounds for adaptive strong approximation of SDEs
- Strong convergence for the Euler-Maruyama approximation of stochastic differential equations with discontinuous coefficients
- Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
- Continuous Markov processes and stochastic equations
- Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
- Exact convergence rate of the Euler-Maruyama scheme, with application to sampling design
- Adaptive time-stepping strategies for nonlinear stochastic systems
- The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
- Optimal approximation of stochastic differential equations by adaptive step-size control
- A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications
- The optimal discretization of stochastic differential equations
