Gauss-Quadrature Method for One-Dimensional Mean-Field SDEs

DOI10.1137/16M1095688zbMath1378.65035arXiv1608.06741MaRDI QIDQ4595786

Tony Shardlow, Peter E. Kloeden

Publication date: 6 December 2017

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.06741

zbMATH Keywords

convergenceinitial value problemGauss quadraturenumerical experimentmean-field stochastic differential equationsMcKean-Vlasov equationsEuler-Maruyama time-stepping method

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 (4)

Numerical methods for mean-field stochastic differential equations with jumps ⋮ Projected Particle Methods for Solving McKean--Vlasov Stochastic Differential Equations ⋮ An Explicit Multistep Scheme for Mean-Field Forward-Backward Stochastic Differential Equations ⋮ Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean

Uses Software

• SDELab
• OPQ

Cites Work

• The mean-square dichotomy spectrum and a bifurcation to a mean-square attractor
• Deterministic quadrature formulas for SDEs based on simplified weak Itô-Taylor steps
• SDELab: A package for solving stochastic differential equations in MATLAB
• Rate of convergence of a particle method to the solution of the McKean-Vlasov equation
• On a perturbation theory and on strong convergence rates for stochastic ordinary and partial differential equations with nonglobally monotone coefficients
• Convergence rate for the approximation of the limit law of weakly interacting particles: Application to the Burgers equation
• Fast computation of Gauss quadrature nodes and weights on the whole real line
• An Introduction to Computational Stochastic PDEs
• Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
• Stochastic Differential Equations with Nonlocal Sample Dependence
• A survey of matrix inverse eigenvalue problems
• On the McKean-Vlasov Limit for Interacting Diffusions
• Generalized Characteristic Polynomials and Gaussian Cubature Rules
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS
• Calculation of Gauss Quadrature Rules
• A stochastic particle method for the McKean-Vlasov and the Burgers equation
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Gauss-Quadrature Method for One-Dimensional Mean-Field SDEs