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Mathematics  2007 

Large Deviations for Riesz Potentials of Additive Processes

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Abstract:

We study functionals of the form \[\zeta_{t}=\int_0^{t}...\int_0^{t} | X_1(s_1)+...+ X_p(s_p)|^{-\sigma}ds_1... ds_p\] where $X_1(t),..., X_p(t)$ are i.i.d. $d$-dimensional symmetric stable processes of index $0<\bb\le 2$. We obtain results about the large deviations and laws of the iterated logarithm for $\zeta_{t}$.

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