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 renormalized self-intersection local times of stable processes." Ann. Probab. 33 (3) 984 - 1013, May 2005. https://doi.org/10.1214/009117904000001099