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Journal of Theoretical Probability

, Volume 24, Issue 2, pp 454–478 | Cite as

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

  • Valentin Konakov
  • Stéphane MenozziEmail author
Article

Abstract

Consider a multidimensional stochastic differential equation of the form \(X_{t}=x+\int_{0}^{t}b(X_{s-})\,ds+\int_{0}^{t}f(X_{s-})\,dZ_{s}\), 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.

Keywords

Symmetric stable processes Parametrix Euler scheme 

Mathematics Subject Classification (2000)

60H30 65C30 60G52 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.CEMIAcademy of SciencesMoscowRussia
  2. 2.LPMAUniversité Paris VII DiderotParisFrance

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