A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise

DOI10.1007/s10543-012-0370-8zbMath1259.65007OpenAlexW2055755622MaRDI QIDQ1759581

Desheng Wang, Xiao-Jie Wang, Si-qing Gan

Publication date: 21 November 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-012-0370-8

zbMATH Keywords

stabilitystrong convergencenumerical experimentsmean-square stabilityalmost sure asymptotic stabilitystiff stochastic differential equationfully implicit Milstein method

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stability and convergence of numerical methods for ordinary differential equations (65L20) Ordinary differential equations and systems with randomness (34F05) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical methods for stiff equations (65L04)

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Uses Software

• RODAS

Cites Work

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• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
• The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations
• A note on the balanced method
• Almost sure exponential stability of numerical solutions for stochastic delay differential equations
• Compensated stochastic theta methods for stochastic differential equations with jumps
• The fully implicit stochastic-\(\alpha \) method for stiff stochastic differential equations
• A review on stochastic differential equations for applications in hydrology
• Almost sure asymptotic stability of drift-implicit \(\theta\)-methods for bilinear ordinary stochastic differential equations in \(\mathbb R^1\)
• Two-stage stochastic Runge-Kutta methods for stochastic differential equations
• Asymptotic mean-square stability of two-step methods for stochastic ordinary differential equations
• Numerical methods for strong solutions of stochastic differential equations: an overview
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation
• THE NUMERICAL SOLUTION OF NONLINEAR STOCHASTIC DYNAMICAL SYSTEMS: A BRIEF INTRODUCTION
• Balanced Implicit Methods for Stiff Stochastic Systems
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Balanced Milstein Methods for Ordinary SDEs
• The composite Euler method for stiff stochastic differential equations
• Implicit Taylor methods for stiff stochastic differential equations

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