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Itô correction terms for the radial parts of semimartingales on manifolds
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  • Published: March 1995

Itô correction terms for the radial parts of semimartingales on manifolds

  • Huiling Le1 &
  • Dennis Barden2 

Probability Theory and Related Fields volume 101, pages 133–146 (1995)Cite this article

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  • 7 Citations

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Summary

We consider functions,F, of a semimartingale,X, on a complete manifold which fail to beC 2 only on, and are sufficiently well-behaved near, a codimension 1 subset ℒ. We obtain an extension of the Itô formula which is valid for all time by adding a continuous predictable process given explicitly in terms of two geometric local times ofX on ℒ and the Gâteaux derivative ofF. We then examine the cut locus of a point of the manifold in sufficient detail to show that this result applies to give a corresponding expression for the radial part of the semimartingale.

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Authors and Affiliations

  1. Department of Mathematics, University of Nottingham, University Park, NG7 2RD, Nottingham, UK

    Huiling Le

  2. Girton College, CB3 0JG, Cambridge, UK

    Dennis Barden

Authors
  1. Huiling Le
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  2. Dennis Barden
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Le, H., Barden, D. Itô correction terms for the radial parts of semimartingales on manifolds. Probab. Th. Rel. Fields 101, 133–146 (1995). https://doi.org/10.1007/BF01192198

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  • Received: 26 January 1994

  • Revised: 08 June 1994

  • Issue Date: March 1995

  • DOI: https://doi.org/10.1007/BF01192198

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Mathematics Subject Classification (1991)

  • 58G32
  • 60H15
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