no. 3
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.

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.

DOI : 10.1214/08-AIHP181
Classification : 60F10, 60F52
Mots clés : large deviations, Riesz potentials, additive processes 
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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://archive.numdam.org/articles/10.1214/08-AIHP181/

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