English

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}
}