Large deviations for renormalized self-intersection local times of stable processes

2005/05/01 by Richard Bass, Richard F. Bass, Xia Chen +1 · 2 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · #Nonlinear Dynamics and Pattern Formation #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:60G52. #msc:60J55

paper · pdf · doi:10.1214/009117904000001099

published as Annals of Probability 2005, Vol. 33, No. 3, 984-1013 · Published at http://dx.doi.org/10.1214/009117904000001099 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2005/05/01 · arxiv created 2005/08/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm

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