# Weak Error for stable driven SDEs: expansion of the densities

Abstract : Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the above equation admits a density w.r.t. the Lebesgue measure and so does its Euler scheme. Using a parametrix approach, we derive an error expansion at order 1 w.r.t. the time step for the difference of these densities.
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Cited literature [13 references]

https://hal.archives-ouvertes.fr/hal-00331845
Contributor : Stephane Menozzi <>
Submitted on : Friday, January 22, 2010 - 4:05:52 PM
Last modification on : Tuesday, May 14, 2019 - 10:27:44 AM
Long-term archiving on : Thursday, September 23, 2010 - 6:15:13 PM

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### Identifiers

• HAL Id : hal-00331845, version 3
• ARXIV : 0810.3224

### Citation

Valentin Konakov, Stephane Menozzi. Weak Error for stable driven SDEs: expansion of the densities. Journal of Theoretical Probability, Springer, 2011, 24 (2), pp.454-478. ⟨hal-00331845v3⟩

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