Convergence Rates of Split-Step Theta Methods for SDEs with Non-Globally Lipschitz Diffusion Coefficients

DOI10.4208/eajam.161121.090722zbMath1515.60254OpenAlexW4313517722MaRDI QIDQ6165526

Xiao-Juan Wu, Si-qing Gan

Publication date: 5 July 2023

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.161121.090722

zbMATH Keywords

stochastic differential equationsplit-step theta methodstrong convergence ratenon-globally Lipschitz coefficient

Mathematics Subject Classification ID

Stochastic partial differential equations (aspects of stochastic analysis) (60H15) 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
• Order-preserving strong schemes for SDEs with locally Lipschitz coefficients
• Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
• Exponential mean square stability of numerical methods for systems of 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
• Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
• A note on tamed Euler approximations
• Convergence rates of the truncated Euler-Maruyama method for stochastic differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Semi-implicit split-step numerical methods for a class of nonlinear stochastic differential equations with non-Lipschitz drift terms
• The truncated Milstein method for stochastic differential equations with commutative noise
• Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
• On Milstein approximations with varying coefficients: the case of super-linear diffusion coefficients
• Split-step theta Milstein methods for SDEs with non-globally Lipschitz diffusion coefficients
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Mean-square convergence rates of stochastic theta methods for SDEs under a coupled monotonicity condition
• Adaptive Euler-Maruyama method for SDEs with nonglobally Lipschitz drift
• Split-step balanced \(\theta \)-method for SDEs with non-globally Lipschitz continuous coefficients
• Tamed Runge-Kutta methods for SDEs with super-linearly growing drift and diffusion coefficients
• Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
• Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise.
• Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
• Strong convergence of split-step theta methods for non-autonomous stochastic differential equations
• An Explicit Euler Scheme with Strong Rate of Convergence for Financial SDEs with Non-Lipschitz Coefficients
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Adaptive time-stepping strategies for nonlinear stochastic systems
• Exponential integrability properties of numerical approximation processes for nonlinear stochastic differential equations
• 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
• Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations
• A Fundamental Mean-Square Convergence Theorem for SDEs with Locally Lipschitz Coefficients and Its Applications
• Strong convergence rates for backward Euler–Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
• Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients