Weak error for stable driven stochastic differential equations: expansion of the densities (Q548158)

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.