Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

DOI10.1112/S1461157012000010zbMath1294.60093MaRDI QIDQ5169628

Evelyn Buckwar, Cónall Kelly, Gregory Berkolaiko, Aleksandra Rodkina

Publication date: 11 July 2014

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

zbMATH Keywords

almost sure asymptotic stability\(\theta\)-Maruyama methodItō differential equation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic stability in control theory (93E15) 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)

Related Items (13)

Numerical preservation issues in stochastic dynamical systems by \(\vartheta\)-methods ⋮ Asymptotic moment boundedness of the stochastic theta method and its application for stochastic differential equations ⋮ Almost sure instability of the equilibrium solution of a Milstein-type stochastic difference equation ⋮ Application of a discrete Itô formula to determine stability (instability) of the equilibrium of a scalar linear stochastic difference equation ⋮ Stationary distribution of the stochastic theta method for nonlinear stochastic differential equations ⋮ On target-oriented control of Hénon and Lozi maps ⋮ Equivalence of stability among stochastic differential equations, stochastic differential delay equations, and their corresponding Euler-Maruyama methods ⋮ Numerical stationary distribution and its convergence for nonlinear stochastic differential equations ⋮ Theta schemes for SDDEs with non-globally Lipschitz continuous coefficients ⋮ The partially truncated Euler-Maruyama method and its stability and boundedness ⋮ Corrigendum: On the use of a discrete form of the Itô formula in the article ‘Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations’ ⋮ A Stable Numerical Scheme for Stochastic Differential Equations with Multiplicative Noise ⋮ Instability and stability of solutions of systems of nonlinear stochastic difference equations with diagonal noise

Cites Work

• Unnamed Item
• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
• Random difference equations and renewal theory for products of random matrices
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• Statistics of Sieves and Square-Free Numbers
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• A DISCRETE-TIME ITÔ'S FORMULA
• Stabilization and Destabilization of Nonlinear Differential Equations by Noise
• Solving Ordinary Differential Equations II
• Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations
• Products of Random Matrices

This page was built for publication: Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations