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Intersection Local Time for Two Independent Fractional Brownian Motions

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Abstract

Let B H and \(\widetilde{B}^{H}\) be two independent, d-dimensional fractional Brownian motions with Hurst parameter H∈(0,1). Assume d≥2. We prove that the intersection local time of B H and \(\widetilde{B}^{H}\)

$$I(B^{H},\widetilde{B}^{H})=\int_{0}^{T}\int_{0}^{T}\delta(B_{t}^{H}-\widetilde{B}_{s}^{H})dsdt$$

exists in L 2 if and only if Hd<2.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS, 66045, USA

    David Nualart

  2. Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007, Barcelona, Spain

    Salvador Ortiz-Latorre

Authors
  1. David Nualart
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  2. Salvador Ortiz-Latorre
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Correspondence to David Nualart.

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Nualart, D., Ortiz-Latorre, S. Intersection Local Time for Two Independent Fractional Brownian Motions. J Theor Probab 20, 759–767 (2007). https://doi.org/10.1007/s10959-007-0106-x

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  • DOI: https://doi.org/10.1007/s10959-007-0106-x

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