Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of   Local Times
  Generalised Ito formulae are proved for time dependent functions of continuous real valued semi-martingales. The conditions involve left space and time first derivatives, with the left space derivative required to have locally bounded 2-dimensional variation. In particular a class of functions with discontinuous first derivative is included. An estimate of Krylov allows further weakening of these conditions when the semi-martingale is a diffusion. 
K.D. Elworthy, A. Truman, H.Z. Zhao