Large deviations for self-intersection local times of stable random walks

2010/03/31 by Laurent, Clément
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1003.6060

Abstract

Let (X_t,t≥ 0) be a random walk on ℤ^d. Let l_T(x)= ∫₀^T δ_x(X_s)ds the local time at the state x and I_T= ∑_x∈ℤ^d l_T(x)^q the q-fold self-intersection local time (SILT). In \citeCastell Castell proves a large deviations principle for the SILT of the simple random walk in the critical case q(d-2)=d. In the supercritical case q(d-2)>d, Chen and Mörters obtain in \citeChenMorters a large deviations principle for the intersection of q independent random walks, and Asselah obtains in \citeAsselah5 a large deviations principle for the SILT with q=2. We extend these results to an α-stable process (i.e. α∈]0,2]) in the case where q(d-α)≥ d.

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