%0 Journal Article %T Continuous Differentiability of Renormalized Intersection Local Times in R^{1} %A Jay S. Rosen %J Mathematics %D 2009 %I arXiv %R 10.1214/09-AIHP338 %X We study $\gamma_{k}(x_2,...,x_k;t)$, the k-fold renormalized self-intersection local time for Brownian motion in $R^1$. Our main result says that $\gamma_{k}(x_2,...,x_k;t)$ is continuously differentiable in the spatial variables, with probability 1. %U http://arxiv.org/abs/0910.2919v1