Large deviations for Riesz potentials of additive processes

Richard Bass; Xia Chen; Jay Rosen

doi:10.1214/08-AIHP181

August 2009 Large deviations for Riesz potentials of additive processes

Richard Bass, Xia Chen, Jay Rosen

Ann. Inst. H. Poincaré Probab. Statist. 45(3): 626-666 (August 2009). DOI: 10.1214/08-AIHP181

Abstract

We study functionals of the form

ζ_t=∫₀^t⋯∫₀^t|X₁(s₁)+⋯+X_p(s_p)|^−σ ds₁ ⋯ ds_p,

where X₁(t), …, X_p(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 ζ_t.

Nous étudions les fonctionelles de la forme

ζ_t=∫₀^t⋯∫₀^t|X₁(s₁)+⋯+X_p(s_p)|^−σ ds₁ ⋯ ds_p,

où X₁(t), …, X_p(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.

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Richard Bass, Xia Chen, and Jay Rosen "Large deviations for Riesz potentials of additive processes," Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 45(3), 626-666, (August 2009). https://doi.org/10.1214/08-AIHP181

Published: August 2009

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