Local time Continuous semi-martingale Generalised Ito formula Two-dimensional Lebusgue-Stieltjes integral
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.