Weak Error for Stable Driven Stochastic Differential Equations: Expansion of the Densities

Valentin Konakov; Stéphane Menozzi

doi:10.1007/s10959-010-0291-x

Weak Error for Stable Driven Stochastic Differential Equations: Expansion of the Densities

Valentin Konakov
, Stéphane Menozzi

Academy of Sciences
Laboratoire de Probabilités et Modèles Aléatoires

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

21 Citations (Scopus)

Résumé

Consider a multidimensional stochastic differential equation of the form X_t = x + ∫₀ ^t b(X_s-)ds + ∫₀ ^t f(X_s-)dZ_s, where (Z_s)_s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to the time step for the difference of these densities.

langue originale	Anglais
Pages (de - à)	454-478
Nombre de pages	25
journal	Journal of Theoretical Probability
Volume	24
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s10959-010-0291-x
état	Publié - 1 juin 2011
Modification externe	Oui

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abstract = "Consider a multidimensional stochastic differential equation of the form Xt = x + ∫0 t b(Xs-)ds + ∫0 t f(Xs-)dZs, where (Zs)s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to the time step for the difference of these densities.",

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N2 - Consider a multidimensional stochastic differential equation of the form Xt = x + ∫0 t b(Xs-)ds + ∫0 t f(Xs-)dZs, where (Zs)s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to the time step for the difference of these densities.

AB - Consider a multidimensional stochastic differential equation of the form Xt = x + ∫0 t b(Xs-)ds + ∫0 t f(Xs-)dZs, where (Zs)s≥0 is a symmetric stable process. Under suitable assumptions on the coefficients, the unique strong solution of the above equation admits a density with respect to Lebesgue measure, and so does its Euler scheme. Using a parametrix approach, we derive an error expansion with respect to the time step for the difference of these densities.

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KW - Symmetric stable processes

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ER -

Weak Error for Stable Driven Stochastic Differential Equations: Expansion of the Densities

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