Almost sure exponential stability of an explicit stochastic orthogonal Runge-Kutta-Chebyshev method for stochastic delay differential equations

DOI10.1186/s13662-015-0642-0zbMath1422.65021OpenAlexW2111878747WikidataQ59434165 ScholiaQ59434165MaRDI QIDQ1622727

Qian Guo, Juan Zhong

Publication date: 19 November 2018

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-015-0642-0

zbMATH Keywords

Chebyshev methodRunge-Kutta methodexplicit schemesalmost sure stabilitystochastic delay differential equationsdiscrete semimartingale convergence theorem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (2)

Delay dependent asymptotic mean square stability analysis of the stochastic exponential Euler method ⋮ Delay dependent stability of stochastic split-step \(\theta\) methods for stochastic delay differential equations

Uses Software

• S-ROCK

Cites Work

• Unnamed Item
• Delay-dependent stability analysis of numerical methods for stochastic delay differential equations
• MS-stability of the Euler--Maruyama method for stochastic differential delay equations
• Exponential stability of equidistant Euler-Maruyama approximations of stochastic differential delay equations
• Almost sure exponential stability of numerical solutions for stochastic delay differential equations
• S-ROCK methods for stiff Itô SDEs
• Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Almost sure asymptotic stability of drift-implicit \(\theta\)-methods for bilinear ordinary stochastic differential equations in \(\mathbb R^1\)
• Numerical solutions of stochastic differential equations -- implementation and stability issues
• Mean square stability and dissipativity of two classes of theta methods for systems of stochastic delay differential equations
• Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations
• Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
• S-ROCK: Chebyshev Methods for Stiff Stochastic Differential Equations
• Almost sure asymptotic stability and convergence of stochastic Theta methods applied to systems of linear SDEs in
• Almost sure exponential stability of the Euler–Maruyama approximations for stochastic functional differential equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations

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