Remarks on the intersection local time of fractional Brownian motions
The existence of the so-called intersection local time \[ I(B^H,\widetilde B^H)\equiv\int_0^T\int_0^T\delta(B_t^H-\widetilde B_s^H)\,ds\,dt, \] where \(\delta(x)\) is the Dirac delta function was given by \textit{D. Nualart} and \textit{S. Ortiz-Latorre} [J. Theor. Probab. 20, No. 4, 759--767 (2007; Zbl 1154.60028)]. The authors give another proof for the existence of the random variable \(I(B^H,\widetilde B^H)\) in \(L^2\). They also discuss necessary and sufficient conditions for the intersection local time process to be smooth in the sense of Meyer-Watanabe.
scientific article; zbMATH DE number 5932052
scientific article