Nous étudions les fonctionelles de la forme ζt=∫0t⋯∫0t|X1(s1)+⋯+Xp(sp)|-σ ds1 ⋯ dsp, où X1(t), …, Xp(t) sont des processus stables symétriques indépendants et identiquement distribués d'ordre 0<β≤2. Nous obtenons des résultats sur les grandes déviations et les lois du logarithme itéré.
We study functionals of the form ζt=∫0t⋯∫0t|X1(s1)+⋯+Xp(sp)|-σ ds1 ⋯ dsp, where X1(t), …, Xp(t) are i.i.d. d-dimensional symmetric stable processes of index 0<β≤2. We obtain results about the large deviations and laws of the iterated logarithm for ζt.
Mots clés : large deviations, Riesz potentials, additive processes
@article{AIHPB_2009__45_3_626_0, author = {Bass, Richard and Chen, Xia and Rosen, Jay}, title = {Large deviations for {Riesz} potentials of additive processes}, journal = {Annales de l'I.H.P. Probabilit\'es et statistiques}, pages = {626--666}, publisher = {Gauthier-Villars}, volume = {45}, number = {3}, year = {2009}, doi = {10.1214/08-AIHP181}, mrnumber = {2548497}, zbl = {1181.60035}, language = {en}, url = {http://www.numdam.org/articles/10.1214/08-AIHP181/} }
TY - JOUR AU - Bass, Richard AU - Chen, Xia AU - Rosen, Jay TI - Large deviations for Riesz potentials of additive processes JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2009 SP - 626 EP - 666 VL - 45 IS - 3 PB - Gauthier-Villars UR - http://www.numdam.org/articles/10.1214/08-AIHP181/ DO - 10.1214/08-AIHP181 LA - en ID - AIHPB_2009__45_3_626_0 ER -
%0 Journal Article %A Bass, Richard %A Chen, Xia %A Rosen, Jay %T Large deviations for Riesz potentials of additive processes %J Annales de l'I.H.P. Probabilités et statistiques %D 2009 %P 626-666 %V 45 %N 3 %I Gauthier-Villars %U http://www.numdam.org/articles/10.1214/08-AIHP181/ %R 10.1214/08-AIHP181 %G en %F AIHPB_2009__45_3_626_0
Bass, Richard; Chen, Xia; Rosen, Jay. Large deviations for Riesz potentials of additive processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 45 (2009) no. 3, pp. 626-666. doi : 10.1214/08-AIHP181. http://www.numdam.org/articles/10.1214/08-AIHP181/
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