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

K. D. Elworthy·A. Truman·H. Z. Zhao
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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.

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K. D. Elworthy, A. Truman, H. Z. Zhao. 2015-08-10. Generalized Ito Formulae and Space-Time Lebesgue-Stieltjes Integrals of Local Times. https://arxiv.org/abs/math/0505195

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