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Itô's formula for C 1,λ-functions of a càdlàg process and related calculus
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  • Published: February 2002

Itô's formula for C 1,λ-functions of a càdlàg process and related calculus

  • Mohammed Errami1,
  • Francesco Russo1 &
  • Pierre Vallois2 

Probability Theory and Related Fields volume 122, pages 191–221 (2002)Cite this article

  • 307 Accesses

  • 26 Citations

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Abstract.

 This article develops a framework of stochastic calculus with respect to a càdlàg finite quadratic variation process. We apply it to the study of a generalization of a semimartingale driven SDE studied by Kurtz, Pardoux and Protter [KPP]. We prove an Itô's formula for functions f(X) of a semimartingale with jumps when f has weak smoothness properties. Examples of X for which this formula is valid are time reversible semimartingales and solutions of [KPP] equations driven by Lévy processes, provided the sum of the absolute values of the jumps, raised to the power 1 + λ, is a.s. finite, where λ takes values between 0 and 1.

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Authors and Affiliations

  1. Université Paris 13, Institut Galilée, Mathématiques, Avenue J.B. Clément, F-93430 Villetaneuse, France. e-mail: russo@math.univ-paris13.fr, , , , , , FR

    Mohammed Errami & Francesco Russo

  2. Université Henri Poincaré Nancy 1, Département de Mathématiques, Institut Elie Cartan, B.P. 239, F-54506 Vandoelig;vre lès Nancy Cedex, France, , , , , , FR

    Pierre Vallois

Authors
  1. Mohammed Errami
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  2. Francesco Russo
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  3. Pierre Vallois
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Received: 1 March 1999 / Revised version: 15 April 2001 / Published online: 11 December 2001

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Errami, M., Russo, F. & Vallois, P. Itô's formula for C 1,λ-functions of a càdlàg process and related calculus. Probab Theory Relat Fields 122, 191–221 (2002). https://doi.org/10.1007/s004400100168

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  • Issue Date: February 2002

  • DOI: https://doi.org/10.1007/s004400100168

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Keywords

  • Variation Process
  • Quadratic Variation
  • Stochastic Calculus
  • Smoothness Property
  • Related Calculus
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