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Mathematics  2009 

Continuous Differentiability of Renormalized Intersection Local Times in R^{1}

DOI: 10.1214/09-AIHP338

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Abstract:

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.

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