Large Deviations for Renormalized Self - Intersection Local times of Stable Processes

Large Deviations for Renormalized Self-intersection Local times of Stable Processes by Richard Bass,1

Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks

We study moderate deviations for the renormalized self-intersection local time of planar random walks. We also prove laws of the iterated logarithm for such local times

Exponential asymptotics for intersection local times of stable processes and random walks

We study large deviations for intersection local times of p independent d-dimensional symmetric stable processes of index β, under the condition p(d − β) < d. Our approach is based on FeynmanKac type large deviations, moment computations and some techniques from probability in Banach spaces.

Derivatives of self-intersection local times

We show that the renormalized self-intersection local time γt(x) for both the Brownian motion and symmetric stable process in R is differentiable in the spatial variable and that γ′ t(0) can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random Schwartz distribution. Analogo...

Large and moderate deviations for intersection local times

We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for the L2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and...