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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.

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
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