# Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times

Research paper by K. D. Elworthy, A. Truman, H. Z. Zhao

Indexed on: 10 Aug '15Published on: 10 Aug '15Published in: Mathematics - Probability

#### Abstract

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.