The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels

H. Abels M. Kassmann

We consider the linear integro-differential operator $L$ defined by \[ Lu(x) =\int_\Rn (u(x+y) - u(x) - 1_{[1,2]}(α) 1_{\{|y|\leq 2\}}(y)y \cdot \nabla u(x)) k(x,y) \sd y . \] Here…