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Stokes and Itô’s Formulae for Anticipative Processes in Two Dimensions with Non-Monotonous Time

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Stochastic Analysis and Related Topics VII

Part of the book series: Progress in Probability ((PRPR,volume 48))

Abstract

In the first part of this work, with the help of a new class of distributions on the Wiener space, we define a surface Skorohod integral on the boundary∂Dof a smooth domainDin ℝd. We establish Stokes’ formula for a smooth random field and deduce Green’s formula. The second part is devoted to proving an Itâtype formula for an anticipative stochastic process with a two parameter non monotonous time scale by using this new class of distributions and the fundamental theorem of differential calculus.

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Author information

Authors and Affiliations

  1. Faculté des Sciences et Techniques Département de Mathématiques, Universite Hassan II-Mohammedia, B.P. 146, Mohammedia, Morroco

    S. Amine

Authors
  1. S. Amine
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Editor information

Editors and Affiliations

  1. Département Réseaux, Ecole Nationale Supérieure des Télécommunications, Paris Cedex 13, 75634, France

    Laurent Decreusefond  & Ali Süleyman Üstünel  & 

  2. Department of Mathematics, University of Oslo, N-0316, Oslo, Norway

    Bernt K. Øksendal

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Amine, S. (2001). Stokes and Itô’s Formulae for Anticipative Processes in Two Dimensions with Non-Monotonous Time. In: Decreusefond, L., Øksendal, B.K., Üstünel, A.S. (eds) Stochastic Analysis and Related Topics VII. Progress in Probability, vol 48. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0157-1_4

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  • DOI: https://doi.org/10.1007/978-1-4612-0157-1_4

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  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-6638-9

  • Online ISBN: 978-1-4612-0157-1

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