Large Deviations for Riesz Potentials of Additive Processes

Abstract

We study functionals of the form \[ζ_{t}=\int_0^{t}...\int_0^{t} | X_1(s_1)+...+ X_p(s_p)|^{-σ}ds_1... ds_p\] 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 ${\zeta }_t$.

References in corpus (1)

• Self-intersection local time: Critical exponent, large deviations, and laws of the iterated logarithm