Parabolic comparison revisited and applications
  We consider the Cauchy-Dirichlet problem $\partial_t u - F(t,x,u,Du,D^2 u) = 0 on (0,T)\times \R^n$ in viscosity sense. Comparison is established for bounded semi-continuous (sub-/super-)solutions under structural assumption (3.14) of the User's Guide plus a mild condition on $F$ such as to cope with the unbounded domain. Comparison on $(0,T]$, space-time regularity and existence are also discussed. Our analysis passes through an extension of the parabolic theorem of sums which appears to be useful in its own right. 
Joscha Diehl, Peter K. Friz and Harald Oberhauser
math.AP math.PR