Remarks on the intersection local time of fractional Brownian motions

Chao Chen and Litan Yan

Statistics & Probability Letters, 2011, vol. 81, issue 8, 1003-1012

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 .

Keywords: Intersection; local; time; Fractional; Brownian; motion; Chaos; expansion (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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