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Séminaire de Probabilités XLIV pp 141–148Cite as

The Derivative of the Intersection Local Time of Brownian Motion Through Wiener Chaos

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Part of the book series: Lecture Notes in Mathematics ((SEMPROBAB,volume 2046))

Abstract

Rosen (Séminaire de Probabilités XXXVIII, 2005) proved the existence of a process known as the derivative of the intersection local time of Brownian motion in one dimension. The purpose of this paper is to use the methods developed in Nualart and Vives (Publicacions Matematiques 36(2):827–836, 1992) in order to give a simple new proof of the existence of this process. Some related theorems and conjectures are discussed.

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References

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Acknowledgements

I would like to thank Paul Jung, David Nualart, and Jay Rosen for helpful conversations. I would also like to thank the referee for comments which improved the exposition. I am grateful for support from the Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (Grant #2009-0094070) and from Australian Research Council Grant DP0988483.

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Authors and Affiliations

  1. Monash University, VIC, Melbourne, 3800, Australia

    Greg Markowsky

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  1. Greg Markowsky
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Correspondence to Greg Markowsky .

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Editors and Affiliations

  1. , Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des États-Unis 45, Versailles, 78035, France

    Catherine Donati-Martin

  2. IECN, Campus scientifique, BP 239, Nancy-Université, INRIA, Vandoeuvre-lès-Nancy, 54506, France

    Antoine Lejay

  3. Laboratoire de Mathématiques, Université de Versailles-St-Quentin, avenue des Etats-Unis 45, Versailles, 78035, France

    Alain Rouault

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Markowsky, G. (2012). The Derivative of the Intersection Local Time of Brownian Motion Through Wiener Chaos. In: Donati-Martin, C., Lejay, A., Rouault, A. (eds) Séminaire de Probabilités XLIV. Lecture Notes in Mathematics(), vol 2046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27461-9_6

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