Bass, Richard F.; Khoshnevisan, Davar Intersection local times and Tanaka formulas. (English) Zbl 0798.60072 Ann. Inst. Henri Poincaré, Probab. Stat. 29, No. 3, 419-451 (1993). Double points of three-dimensional Brownian motion and \(k\)-multiple points of two-dimensional Brownian motion for every positive integer \(k\) are considered. Then a local time for these multiple points, that is, a functional that increases only at the times when Brownian motion has a multiple point, is constructed. A new approach to intersection local times (ILT) of Brownian motion is given by using additive functionals of a single Markov process and stochastic calculus. New results include the Tanaka formula for the \(k\)-multiple points of self-intersection local time. It is also proved that one can renormalize ILT for \(k\)-multiple points in terms of lower order ILTs in such a way that the renormalized ILT is jointly Hölder continuous in every variable almost surely for every \(k>1\). Reviewer: M.N.Sviridenko (Moskva) Cited in 13 Documents MSC: 60J55 Local time and additive functionals 60J65 Brownian motion Keywords:renormalization; multiple points; double points; intersection local times; Brownian motion; additive functionals; Tanaka formula PDFBibTeX XMLCite \textit{R. F. Bass} and \textit{D. Khoshnevisan}, Ann. Inst. Henri Poincaré, Probab. Stat. 29, No. 3, 419--451 (1993; Zbl 0798.60072) Full Text: Numdam EuDML