Large deviations and laws of the iterated logarithm for the local times of additive stable processes
Chen, Xia
Ann. Probab., Tome 35 (2007) no. 1, p. 602-648 / Harvested from Project Euclid
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We study the upper tail behaviors of the local times of the additive stable processes. Let X1(t), …, Xp(t) be independent, d-dimensional symmetric stable processes with stable index 0<α≤2 and consider the additive stable process X̅(t1, …, tp)=X1(t1)+⋯+Xp(tp). Under the condition d<αp, we obtain a precise form of the large deviation principle for the local time ¶ ηx([0, t]p)=∫0t⋯∫0tδx(X1(s1)+⋯+Xp(sp)) ds1⋯ dsp ¶ of the multiparameter process X̅(t1, …, tp), and for its supremum norm sup x∈ℝdηx([0, t]p). Our results apply to the law of the iterated logarithm and our approach is based on Fourier analysis, moment computation and time exponentiation.
Publié le : 2007-03-14
Classification:  Additive stable process,  local time,  law of the iterated logarithm,  large deviations,  60F10,  60F15,  60J55,  60G52 
@article{1175287756,
     author = {Chen, Xia},
     title = {Large deviations and laws of the iterated logarithm for the local times of additive stable processes},
     journal = {Ann. Probab.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 602-648},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175287756}
}

Chen, Xia. Large deviations and laws of the iterated logarithm for the local times of additive stable processes. Ann. Probab., Tome 35 (2007) no. 1, pp.  602-648. http://gdmltest.u-ga.fr/item/1175287756/