The truncated Milstein method for stochastic differential equations with commutative noise

DOI10.1016/j.cam.2018.01.014zbMath1503.65014arXiv1704.04135OpenAlexW2783875654MaRDI QIDQ1743967

Rong-Xian Yue, Wei Liu, Qian Guo, Xuerong Mao

Publication date: 16 April 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1704.04135

zbMATH Keywords

strong convergence ratenon-global Lipschitz conditionnonlinear stochastic differential equations with commutative noisetruncated Milstein method

Mathematics Subject Classification ID

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)

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Cites Work

• Unnamed Item
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• Stochastic Runge-Kutta methods with deterministic high order for ordinary differential equations
• 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
• The partially truncated Euler-Maruyama method and its stability and boundedness
• Convergence and stability of the semi-tamed Euler scheme for stochastic differential equations with non-Lipschitz continuous coefficients
• Supplement: Efficient weak second order stochastic Runge-Kutta methods for non-commutative Stratonovich stochastic differential equations
• Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
• First order strong approximations of scalar SDEs defined in a domain
• A note on tamed Euler approximations
• Weak order stochastic Runge-Kutta methods for commutative stochastic differential equations
• Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
• Numerical solution of stochastic differential equations with jumps in finance
• The fully implicit stochastic-\(\alpha \) method for stiff stochastic differential equations
• Runge-Kutta methods for Stratonovich stochastic differential equation systems with commutative noise.
• A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
• Implicit stochastic Runge-Kutta methods for stochastic differential equations
• Weak second-order stochastic Runge-Kutta methods for non-commutative stochastic differential equations
• Basic Concepts of Numerical Analysis of Stochastic Differential Equations Explained by Balanced Implicit Theta Methods
• Strong convergence of split-step theta methods for non-autonomous stochastic differential equations
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Stochastic ordinary differential equations in applied and computational mathematics
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Multilevel Monte Carlo Path Simulation
• Modeling with Itô Stochastic Differential Equations
• Approximate Integration of Stochastic Differential Equations
• Balanced Implicit Methods for Stiff Stochastic Systems
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
• An Euler-type method for the strong approximation of the Cox–Ingersoll–Ross process
• Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
• Stochastic differential equations. An introduction with applications.

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