Weak error for stable driven stochastic differential equations: expansion of the densities

DOI10.1007/s10959-010-0291-xzbMath1235.60065OpenAlexW1871431569MaRDI QIDQ548158

Stéphane Menozzi, Valentin Konakov

Publication date: 28 June 2011

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-010-0291-x

zbMATH Keywords

parametrixEuler schemesymmetric stable processes

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Numerical solutions to stochastic differential and integral equations (65C30) Stable stochastic processes (60G52)

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Cites Work

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• Weak error for stable driven stochastic differential equations: expansion of the densities
• Explicit parametrix and local limit theorems for some degenerate diffusion processes
• Euler scheme and tempered distributions
• A numerical approximation of parabolic stochastic partial differential equations driven by a Poisson random measure
• The Euler scheme for Lévy driven stochastic differential equations
• The Euler scheme for Lévy driven stochastic differential equations: limit theorems.
• The law of the Euler scheme for stochastic differential equations. I: Convergence rate of the distribution function
• On the existence of smooth densities for jump processes
• The approximate Euler method for Lévy driven stochastic differential equations
• First exit times of SDEs driven by stable Lévy processes
• Curvature and the eigenvalues of the Laplacian
• Approximation of stochastic differential equations driven by α-stable Lévy motion
• Symmetric Stable Laws and Stable-Like Jump-Diffusions
• Error Analysis for Approximation of Stochastic Differential Equations Driven by Poisson Random Measures
• The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density
• Edgeworth type expansions for Euler schemes for stochastic differential equations.
• Expansion of the global error for numerical schemes solving stochastic differential equations