The intersection local time of fractional Brownian motion in the plane (Q1096249)

Let \(X=(X_ t\), \(t\geq 0)\) be a fractional Brownian motion of index \(\beta\) in the plane. The case \(\beta =\) corresponds to the usual planar Brownian motion. For \(1/2<\beta <3/4\), the author proves the existence of a renormalized self-intersection local time of the process X, thus generalizing a result due to \textit{S. R. S. Varadhan} [Appendix to K. Symanzik, Euclidean quantum field theory. in R. Jost (ed.), Local quantum theory, Academic Press, New York (1969)] in the case \(\beta =\). The proofs rely on direct computations using in an essential way the fact that X is a Gaussian process.