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Remarks on the intersection local time of fractional Brownian motions

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  • Chen, Chao
  • Yan, Litan

Abstract

Let BH and be two independent d-dimensional fractional Brownian motions with Hurst parameter H[set membership, variant](0,1). Assume that d>=2. In this paper we consider the so-called intersection local time where [delta] denotes the Dirac delta function. We prove the existence of the random variable in L2. As a related problem, we also discuss the necessary and sufficient conditions for to be smooth in the sense of Meyer-Watanabe. The condition says that it is smooth if and only if .

Suggested Citation

  • Chen, Chao & Yan, Litan, 2011. "Remarks on the intersection local time of fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1003-1012, August.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:8:p:1003-1012
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    References listed on IDEAS

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    1. Rosen, Jay, 1987. "The intersection local time of fractional Brownian motion in the plane," Journal of Multivariate Analysis, Elsevier, vol. 23(1), pages 37-46, October.
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