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Weak error for stable driven stochastic differential equations: expansion of the densities. (English) Zbl 1235.60065
Consider the stochastic differential equation $X_t=x+\int_0^t b(X_s)\, ds+\int_0^tf(X_{s-})dZ_s,\quad 0\leq t\leq T$ for a symmetric stable process $$Z$$, and the Euler approximation $$X_t^N$$ for a time step $$h=T/N$$. Under suitable assumptions, the laws of $$X_T$$ and $$X_T^N$$ have densities $$p(T,x,y)$$ and $$p^N(T,x,y)$$, and by means of a parametrix approach, an expansion of $$p-p^N$$ in powers of $$h$$ is obtained.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H30 Applications of stochastic analysis (to PDEs, etc.) 65C30 Numerical solutions to stochastic differential and integral equations 60G52 Stable stochastic processes
##### Keywords:
symmetric stable processes; parametrix; Euler scheme
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##### References:
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