Stability of the drift-implicit and double-implicit Milstein schemes for nonlinear SDEs

DOI10.1016/j.amc.2018.07.026zbMath1429.65023OpenAlexW2885063282MaRDI QIDQ2007526

Jinran Yao, Si-qing Gan

Publication date: 22 November 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2018.07.026

zbMATH Keywords

stochastic differential equations (SDEs)contractivity in mean squarestability in mean squaredouble-implicit Milstein schemedrift-implicit Milstein scheme

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) 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 (7)

Mean-square contractivity of stochastic \(\vartheta\)-methods ⋮ Strong convergence of an adaptive time-stepping Milstein method for SDEs with monotone coefficients ⋮ Polynomial Propagation of Moments in Stochastic Differential Equations ⋮ Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients ⋮ Split-step balanced \(\theta \)-method for SDEs with non-globally Lipschitz continuous coefficients ⋮ Convergence and stability of the semi-tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients ⋮ Strong convergence of a GBM based tamed integrator for SDEs and an adaptive implementation

Cites Work

• Unnamed Item
• Unnamed Item
• Order-preserving strong schemes for SDEs with locally Lipschitz coefficients
• Convergence, nonnegativity and stability of a new Milstein scheme with applications to finance
• Stability of analytical and numerical solutions of nonlinear stochastic delay differential equations
• Exponential mean square stability of numerical methods for systems of stochastic differential equations
• Split-step Milstein methods for multi-channel stiff stochastic differential systems
• First order strong approximations of scalar SDEs defined in a domain
• Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space
• Stability of numerical methods for delay differential equations
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Convergence and stability of two classes of theta-Milstein schemes for stochastic differential equations
• The truncated Milstein method for stochastic differential equations with commutative noise
• A family of fully implicit Milstein methods for stiff stochastic differential equations with multiplicative noise
• Stable strong order 1.0 schemes for solving stochastic ordinary differential equations
• Two-step Milstein schemes for stochastic differential equations
• Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
• Numerical methods for nonlinear stochastic differential equations with jumps
• Exponential stability in \(p\)-th mean of solutions, and of convergent Euler-type solutions, of stochastic delay differential equations
• Stability analysis of solutions to nonlinear stiff Volterra functional differential equations in Banach spaces
• Continuous Markov processes and stochastic equations
• Discrete approximation of stochastic differential equations
• Double-implicit and split two-step Milstein schemes for stochastic differential equations
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Approximate Integration of Stochastic Differential Equations
• Balanced Implicit Methods for Stiff Stochastic Systems
• Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations
• The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
• Split-step Adams–Moulton Milstein methods for systems of stiff stochastic differential equations
• Stability Analysis of Numerical Schemes for Stochastic Differential Equations
• Balanced Milstein Methods for Ordinary SDEs

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