Numerical approximation of diffusions in \(\mathbb {R}^d\) using normal charts of a Riemannian manifold

DOI10.1016/j.spa.2006.02.004zbMath1101.58023OpenAlexW2080930962WikidataQ115341184 ScholiaQ115341184MaRDI QIDQ2507672

Paul Malliavin, Ana Bela Cruzeiro

Publication date: 5 October 2006

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2006.02.004

zbMATH Keywords

stochastic differential equations on manifoldsMilstein numerical schemesnumerical approximation of stochastic differential equations

Mathematics Subject Classification ID

Diffusion processes and stochastic analysis on manifolds (58J65)

Related Items (3)

HIGHER-ORDER RUNGE-KUTTA METHOD FOR ITÔ STOCHASTIC DIFFERENTIAL EQUATIONS WITH A NON-DEGENERATE DIFFUSION MATRIX ⋮ TWO-STEP ORDER STRONG METHOD FOR APPROXIMATING STOCHASTIC DIFFERENTIAL EQUATIONS ⋮ Geometric Euler--Maruyama Schemes for Stochastic Differential Equations in SO(n) and SE(n)

Cites Work

• Stochastic analysis on the path space of a Riemannian manifold. I: Markovian stochastic calculus
• Numerical error for SDE: Asymptotic expansion and hyperdistributions
• Geometrization of Monte-Carlo numerical analysis of an elliptic operator: Strong approximation
• Renormalized differential geometry on path space: Structural equation, curvature
• Monte-Carlo simulation of stochastic differential systems - a geometrical approach
• Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
• Approximation of Lyapunov Exponents of Nonlinear Stochastic Differential Equations
• Expansion of the global error for numerical schemes solving stochastic differential equations

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