Large deviations and renormalization for Riesz potentials of stable intersection measures

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:120

Article

Chen, Xia²  Rosen, Jay¹ 

[1] CUNY Coll Staten Isl, Dept Math, Staten Isl, NY 10314 USA

[2] Univ Tennessee, Dept Math, Knoxville, TN 37996 USA

关键词: Large deviations;    Renormalization;    Riesz potentials;    Stable intersection measure;   

DOI  :  10.1016/j.spa.2010.05.006

来源: Elsevier

【 摘 要 】

We study the object formally defined as gamma([0, t](2)) =integral integral([0, t]2) vertical bar X-s - X-r vertical bar(-sigma) dr ds - E integral integral([0, t]2) vertical bar X-s - X-r vertical bar(-sigma) dr ds, (0.1) where X-t denotes the symmetric stable processes of index 0 < beta <= 2 in R-d. When beta <= sigma < min{3/2 beta, d}, this has to be defined as a limit, in the spirit of renormalized self-intersection local time. We obta'n results about the large deviations and laws of the iterated logarithm for gamma. This is applied to obtain results about stable processes in random potentials. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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