Intersection Local Time for Two Independent Fractional Brownian Motions

David Nualart () and Salvador Ortiz-Latorre ()
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David Nualart: University of Kansas
Salvador Ortiz-Latorre: Universitat de Barcelona

Journal of Theoretical Probability, 2007, vol. 20, issue 4, 759-767

Abstract: 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

Keywords: Fractional Brownian motion; Intersection local time; 60G15; 60F25; 60G18; 60J55 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10959-007-0106-x

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