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.
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
