Generalized 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 two-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. AMS 2000 subject classifications: 60H05, 60H30 Key words: Local time, Continuous semi-martingale, Generalized Ito’s formula, Two-dimensional Lebesgue–Stieltjes integral
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Elworthy, K.D., Truman, A., Zhao, H. (2007). Generalized Itǒ Formulae and Space-Time Lebesgue–Stieltjes Integrals of Local Times. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XL. Lecture Notes in Mathematics, vol 1899. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71189-6_5
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DOI: https://doi.org/10.1007/978-3-540-71189-6_5
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