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

Valentin Konakov () and Stéphane Menozzi ()
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Valentin Konakov: Academy of Sciences
Stéphane Menozzi: Université Paris VII Diderot

Journal of Theoretical Probability, 2011, vol. 24, issue 2, 454-478

Abstract: 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; 60H30; 65C30; 60G52 (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s10959-010-0291-x

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