Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times
Probability
2015-08-11 v2
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.
Keywords
Cite
@article{arxiv.math/0505195,
title = {Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times},
author = {K. D. Elworthy and A. Truman and H. Z. Zhao},
journal= {arXiv preprint arXiv:math/0505195},
year = {2015}
}