REFLECTED DIFFUSION WITH JUMP AND OBLIQUE REFLECTION

Let ($G,\;{\upsilon}$) be a bounded smooth domain and reflection vector field on $\partial$G, which points uniformly into G. Under the condition that locally for some coordinate system, ${\mid}{\upsilon^i}{\mid}\;i\;=\;1,{\cdot},{\cdot}$,d - 1, where is constant depending on the Lipschitz constant of G, we have tightness for reflected diffusion with jump on G with reflection $\upsilon$ depending only on c. From this, we obtain some properties of L-harmonic function where L is a sum of Laplacian and integro one.