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A remark on the proof of Itô's formula for C2 functions of continuous semimartingales

Part of: Markov processes Stochastic analysis

Published online by Cambridge University Press:  14 July 2016

Wilfrid S. Kendall
Wilfrid S. Kendall*
Affiliation:
University of Warwick
*
∗ Postal address: Department of Statistics, University of Warwick, Coventry CV4 7AL, UK.
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Abstract

The Itô formula is the fundamental theorem of stochastic calculus. This short note presents a new proof of Itô's formula for the case of continuous semimartingales. The new proof is more geometric than previous approaches, and has the particular advantage of generalizing immediately to the multivariate case without extra notational complexity.

Keywords

STOCHASTIC CALCULUSINTEGRATION BY PARTS

MSC classification

Primary: 60H20: Stochastic integral equations
Secondary: 60J65: Brownian motion

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 216 - 221
Copyright
Copyright © Applied Probability Trust 1992 

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References

Ikeda, N. and Watanabe, S. (1981) Stochastic Differential Equations and Diffusion Processes. North-Holland/Kodansha, Amsterdam/Tokyo.Google Scholar
Kendall, W. S. (1987) The radial part of Brownian motion on a manifold: semimartingale properties. Ann. Prob. 15, 1491–1500.Google Scholar
Kendall, W. S. (1988) Symbolic computation and the diffusion of shapes of triads. Adv. Appl. Prob. 20, 775–797.Google Scholar
Kendall, W. S. (1990) The diffusion of Euclidean shape. In Disorder in Physical Systems, ed. Grimmett, G. and Welsh, D., pp. 203–217, Oxford University Press.Google Scholar
Kendall, W. S. (1989) Itô Calculus: Theory, Computer Algebra, Simulation. Unpublished manuscript, Department of Statistics, University of Warwick.Google Scholar
Rogers, L. C. G. and Williams, D. (1987) Diffusions, Markov Processes, and Martingales, Volume 2. Wiley, Chichester.Google Scholar