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An Extension of Ito’s Differentiation Formula

Published online by Cambridge University Press:  22 January 2016

Ata N. Al-Hussaini  and
Robert J. Elliott
Ata N. Al-Hussaini
Affiliation:
Department of Statistics and Applied Probability University of Alberta, Edmonton, Canada T6G 2G1
Robert J. Elliott
Affiliation:
Department of Statistics and Applied Probability University of Alberta, Edmonton, Canada T6G 2G1
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Introduction 1. If denotes the local time of a continuous semi-martingale X at a Bouleau and Yor [1] have obtained a form of Ito’s differentiation formula which states that for absolutely continuous functions F(x)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 9 - 18
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

[ 1 ] Bouleau, N. and Yor, M., Sur la variation quadratique des temps locaux de certaines semimartingales, C.R. Acad. Sci. Paris, 292 (1981), 491–494.Google Scholar
[ 2 ] Meyer, P. A., Un cours sur les integrales stochastiques, Sem de Probabilités X, Lee. Notes in Math., 511, 245–400.Google Scholar
[ 3 ] Perkins, E., Local time is a semimartingale, Z. Wahrsch. Verw. Gebiete, 60 (1982), 79–117.Google Scholar
[ 4 ] Yamada, T., On some representations concerning stochastic integrals, to appear.Google Scholar
[ 5 ] Yor, M., Sur la transformation de Hilbert des temps locaux Browniens, et une extension de la Formule d’Ito, Sem de Probabilités XVI, Lee. Notes in Math., 920, 238–247.Google Scholar