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

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  • Laurent, Clément

Abstract

Let (Xt,t>=0) be a random walk on . Let be the local time at the state x and the q-fold self-intersection local time (SILT). In [5] 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 [10] a large deviations principle for the intersection of q independent random walks, and Asselah obtains in [1] a large deviations principle for the SILT with q=2. We extend these results to an [alpha]-stable process (i.e. [alpha][set membership, variant]]0,2]) in the case where q(d-[alpha])>=d.

Suggested Citation

  • Laurent, Clément, 2010. "Large deviations for self-intersection local times of stable random walks," Stochastic Processes and their Applications, Elsevier, vol. 120(11), pages 2190-2211, November.
  • Handle: RePEc:eee:spapps:v:120:y:2010:i:11:p:2190-2211
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    Cited by:

    1. Yan, Litan & Yu, Xianye & Chen, Ruqing, 2017. "Derivative of intersection local time of independent symmetric stable motions," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 18-28.

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