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Integration par parties dans l'espace de Wiener et approximation du temps local
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  • Published: March 1991

Integration par parties dans l'espace de Wiener et approximation du temps local

  • David Nualart1 &
  • Mario Wschebor2 

Probability Theory and Related Fields volume 90, pages 83–109 (1991)Cite this article

Summary

Let

be a real-valued stochastic process having a continuous local timeL(u,t),u∈ —, 0≦t≦T andX ε(t) = (Ψ ε *X)(t),t ⪴ 0, the regularization ofX by means of the convolution with the approximation of unityΨ ε. The main theorem in this paper (Theorem 3.5) is a generalization of various results about the approximation (for fixedu) of the local timeL(u, •) by means of a convenient normalization of the numberN X ε (u;•) of crossings of the processX ε with the levelu. Especially, this Theorem extends to a class of not necessarily Markovian continuous martingales, a result of this type for one-dimensional diffusions due to Azais [A2]). The methods of proof combine some estimations of the moments of the number of crossings with a level of a regular stochastic processes with stochastic analysis techniques based upon integration by parts in the Wiener space.

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Author information

Authors and Affiliations

  1. Facultat de Matemàtiques, Universitat de Barcelona, Espana

    David Nualart

  2. Centro de Mathemática, Facultad de Ciencias, Universidad de la Republica, Montevideo, Uruguay

    Mario Wschebor

Authors
  1. David Nualart
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  2. Mario Wschebor
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Support partill du CICYT, No PB86-0238

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Nualart, D., Wschebor, M. Integration par parties dans l'espace de Wiener et approximation du temps local. Probab. Th. Rel. Fields 90, 83–109 (1991). https://doi.org/10.1007/BF01321135

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  • Received: 28 August 1990

  • Revised: 13 March 1991

  • Issue Date: March 1991

  • DOI: https://doi.org/10.1007/BF01321135

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