Intersection local times for interlacements

We define renormalized intersection local times for random interlacements of L\'evy processes in R^{d} and prove an isomorphism theorem relating renormalized intersection local times with associated Wick polynomials.Comment: SPA, to appea

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

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

A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes

We provide a sufficient condition for the continuity of real valued permanental processes. When applied to the subclass of permanental processes which consists of squares of Gaussian processes, we obtain the sufficient condition for continuity which is also known to be necessary. Using an isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and permanental processes, we obtain a general sufficient condition for the joint continuity of local times.Comment: Published in at http://dx.doi.org/10.1214/12-AOP744 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org