On the conservative character of discretizations to Itô-Hamiltonian systems with small noise

DOI10.1016/j.aml.2022.108529OpenAlexW4313216508MaRDI QIDQ2677881

Yanyan Li

Publication date: 6 January 2023

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2022.108529

zbMATH Keywords

stochastic numerical methodsperturbative theorysmall noisestochastic Hamiltonian problems

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (2)

Numerical conservation issues for the stochastic Korteweg-de Vries equation ⋮ Random periodic solutions of SDEs: existence, uniqueness and numerical issues

Cites Work

• Unnamed Item
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• Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise
• Locally linearized methods for the simulation of stochastic oscillators driven by random forces
• Stochastic Hamiltonian dynamical systems
• Diffusion in Hamiltonian systems with a small stochastic perturbation
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Numerical preservation of long-term dynamics by stochastic two-step methods
• Numerical simulation of a linear stochastic oscillator with additive noise
• Symplectic integrators to stochastic Hamiltonian dynamical systems derived from composition methods
• Drift-preserving numerical integrators for stochastic Hamiltonian systems
• Exponential mean-square stability properties of stochastic linear multistep methods
• Positivity preserving stochastic \(\theta\)-methods for selected SDEs
• Nonlinear stability issues for stochastic Runge-Kutta methods
• On the numerical structure preservation of nonlinear damped stochastic oscillators
• Perturbative analysis of stochastic Hamiltonian problems under time discretizations
• Energy conservative stochastic difference scheme for stochastic Hamilton dynamical systems
• Weak backward error analysis for stochastic Hamiltonian systems
• Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise
• Mean-square contractivity of stochastic \(\vartheta\)-methods
• Order conditions for sampling the invariant measure of ergodic stochastic differential equations on manifolds
• Conservative methods for stochastic differential equations with a conserved quantity
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Symplectic Integration of Hamiltonian Systems with Additive Noise
• Strong Convergence of Euler-Type Methods for Nonlinear Stochastic Differential Equations
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Drift-preserving numerical integrators for stochastic Poisson systems
• High-Order Symplectic Schemes for Stochastic Hamiltonian Systems
• Numerical methods for Hamiltonian PDEs

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