High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients

DOI10.1002/mma.3647zbMath1338.65010OpenAlexW2279838437MaRDI QIDQ2814094

Chao Yue

Publication date: 17 June 2016

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.3647

zbMATH Keywords

strong convergencestochastic differential equationsone-sided Lipschitz conditionimproved split-step theta methodssuperlinearly growing condition

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items (5)

Improving split-step forward methods by ODE solver for stiff stochastic differential equations ⋮ Split-step theta Milstein methods for SDEs with non-globally Lipschitz diffusion coefficients ⋮ Solving the stochastic differential systems with modified split-step Euler-Maruyama method ⋮ Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations ⋮ Convergence and asymptotic stability of an explicit numerical method for non-autonomous stochastic differential equations

Cites Work

• Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
• A structural analysis of asymptotic mean-square stability for multi-dimensional linear stochastic differential systems
• 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
• Theory of stochastic differential equations with jumps and applications.
• B-convergence of split-step one-leg theta methods for stochastic differential equations
• Continuous Markov processes and stochastic equations
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• The improved split-step θ methods for stochastic differential equation
• Strong convergence of split-step theta methods for non-autonomous stochastic differential equations
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• 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
• 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

This page was built for publication: High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients