Rosen, Jay Derivatives of self-intersection local times. (English) Zbl 1063.60110 Émery, Michel (ed.) et al., 38th seminar on probability. Dedicated Jacques Azéma on the occasion on his 65th birthday. Berlin: Springer (ISBN 3-540-23973-1/pbk). Lecture Notes in Mathematics 1857, 263-281 (2005). Summary: We show that the renormalized self-intersection local time \(\gamma_t(x)\) for both the Brownian motion and symmetric stable process in \(R^1\) is differentiable in the spatial variable and that \(\gamma_t'(0)\) can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dririchlet process is the potential of a random Schwartz distribution. Analogous results for fractional derivatives of self-intersection local times in \(R^1\) and \(R^2\) are also discussed.For the entire collection see [Zbl 1055.60001]. Cited in 3 ReviewsCited in 20 Documents MSC: 60J55 Local time and additive functionals 60G52 Stable stochastic processes 60J65 Brownian motion Keywords:renormalized self-intersection local time; Brownian motion; symmetric stable process; Dririchlet process PDFBibTeX XMLCite \textit{J. Rosen}, Lect. Notes Math. 1857, 263--281 (2005; Zbl 1063.60110)