Non-local Dirichlet forms and symmetric jump processes
Martin T. Barlow, Richard F. Bass, Zhen-Qing Chen, Moritz Kaßmann · Transactions of the American Mathematical Society · 2008
We consider the non-local symmetric Dirichlet form ( E , F ) (\mathcal {E}, \mathcal {F}) given by \[ E ( f , f ) = ∫ R d ∫ R d ( f ( y ) − f ( x ) ) 2 J ( x , y ) d x d y \mathcal {E} (f,f)=\int \limits _{\mathbb {R}^d} \int \limits _{\mathbb {R}^d} (f(y)-f(x))^2 J(x,y) \, dx\, dy \] with F \mathcal {F} the closure with respect to E 1 \mathcal {E}_1 of the set of C 1 C^1 functions on R d \mathbb {R}^d with compact support, where E 1 ( f , f ) := E ( f <