Self-Intersection Local Time of $(\alpha,d,\beta)$-superprocess
  The existence of self-intersection local time (SILT), when the time diagonal is intersected, of the $(\alpha,d,\beta)$-superprocess is proved for $d/2<\alpha $ and for a renormalized SILT when $d/(2+(1+\beta)^{-1})<\alpha \leq d/2$. We also establish Tanaka-like formula for SILT. 
L. Mytnik, J. Villa