Geometrization of Monte-Carlo numerical analysis of an elliptic operator: Strong approximation

DOI10.1016/j.crma.2004.01.007zbMath1046.65006OpenAlexW2120279233MaRDI QIDQ1433391

Anton Thalmaier, Paul Malliavin, Ana Bela Cruzeiro

Publication date: 15 June 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: http://orbilu.uni.lu/handle/10993/13723

zbMATH Keywords

Monte Carlo methodMilstein schemeItô integralsone-step scheme

Mathematics Subject Classification ID

Monte Carlo methods (65C05) 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)

Related Items (11)

HIGHER-ORDER RUNGE-KUTTA METHOD FOR ITÔ STOCHASTIC DIFFERENTIAL EQUATIONS WITH A NON-DEGENERATE DIFFUSION MATRIX ⋮ Weak Milstein scheme without commutativity condition and its error bound ⋮ The implementation of Milstein scheme in two-dimensional SDEs using the Fourier method ⋮ Total variation bound for Milstein scheme without iterated integrals ⋮ The implementation of approximate coupling in two-dimensional SDEs with invertible diffusion terms ⋮ Pathwise optimal transport bounds between a one-dimensional diffusion and its Euler scheme ⋮ Monte-Carlo simulation of stochastic differential systems - a geometrical approach ⋮ Numerical approximation of diffusions in \(\mathbb {R}^d\) using normal charts of a Riemannian manifold ⋮ THE IMPLEMENTATION OF MILSTEIN SCHEME IN TWO-DIMENSIONAL SDES USING NON-DEGENERACY FOR THE DIFFUSION TERM ⋮ Improved local approximation for multidimensional diffusions: The G-rates ⋮ Approximation of SDE solutions using local asymptotic expansions

Cites Work

• Higher-order implicit strong numerical schemes for stochastic differential equations
• Numerical error for SDE: Asymptotic expansion and hyperdistributions
• Convergence to equilibrium for granular media equations and their Euler schemes
• Renormalized differential geometry on path space: Structural equation, curvature
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