Large Deviations for Local Times of Stable Processes and Stable Random Walks in 1 Dimension

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

Large Deviations and Laws of the Iterated Logarithm for the Local times of Additive Stable Processes

We study the upper tail behaviors of the local times of the additive stable processes. Let X1(t), · · · , Xp(t) be independent, d-dimensional symmetric stable processes with stable index 0 < α ≤ 2 and consider the additive stable process X(t1, · · · , tp) = X1(t1) + · · · + Xp(tp). Under the condition d < αp, we obtain a precise form of large deviation principle for the local time

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.

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

We study large deviations for the renormalized self-intersection local time of d-dimensional stable processes of index β ∈ (2d/3, d]. We find a difference between the upper and lower tail. In addition, we find that the behavior of the lower tail depends critically on whether β < d or β = d.

Large deviations for intersection local times in critical dimension

Let (X t , t ≥ 0) be a continuous time simple random walk on Z d , and let l T (x) be the time spent by (X t , t ≥ 0) on the site x up to time T. We prove a large deviations principle for the q-fold self-intersection local time I T = x∈Z d l T (x) q in the critical dimension d = 2q q−1. When q is integer, we obtain similar results for the intersection local times of q independent simple random ...