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Large deviations and laws of the iterated logarithm for the local times of additive stable processes. (English) Zbl 1121.60025

The main aim of this paper is to present the large deviations and the laws of the iterated logarithm for the local times of the \(d\)-dimensional symmetric and additive stable processes. In particular, the author identifies, as much as he can, the constants appearing in these limit forms. The results presented are applied to the law of the iterated logarithm and the approach is based on Fourier analysis, moment computation and time exponentiation.

MSC:

60F10 Large deviations
60F15 Strong limit theorems
60J55 Local time and additive functionals
60G52 Stable stochastic processes
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