Small time asymptotics of diffusion processes
  We establish the short-time asymptotic behaviour of the Markovian semigroups associated with strongly local Dirichlet forms under very general hypotheses. Our results apply to a wide class of strongly elliptic, subelliptic and degenerate elliptic operators. In the degenerate case the asymptotics incorporate possible non-ergodicity. 
A.F.M. ter Elst, Derek W. Robinson, Adam Sikora