Intersection local times as generalized white noise functionals (Q1355861)

Let \(B(t)\) be \(d\)-dimensional Brownian motion, \(L\equiv \int d^2t\delta(B(t_2)-B(t_1))\) be the self-intersection local time of \(B\) represented as an integral over Dirac's or Donsker's \(\delta\)-function. For any \(d>1\) the expansion of \(L\) in terms of ``Wick powers'' of white noise is obtained. This expansion corresponds to that in terms of the multiple Wiener integrals. It occurs that kernel functions of such expansion are remarkably simple and exhibit clearly the dimension dependent singularities of \(L\). The authors calculate they in closed form and discuss their \(L_p\) properties.