Explosion problems for symmetric diffusion processes (Q1057573)

Let L be a strictly elliptic partial differential operator with measurable coefficients of the form \[ L=b^{- 1}\sum^{n}_{i,j=1}\frac{\partial}{\partial x_ i}(a_{ij}\frac{\partial}{\partial x_ j}). \] Denote by \((X_ t,\zeta,P_ x)\) the unique minimal diffusion process generated by L, where \(\zeta\) is the explosion time. The author states several theorems giving criteria for \(P_ x(\xi =+\infty)=1\) and for explosion in finite time in terms of capacities and of the coefficients of L. No proofs are given.