Large deviations for discontinuous additive functionals of symmetric stable processes



Let Xt be a symmetric stable process on d-dimensional Euclidean space equation image. Let F(x, y) be a symmetric positive bounded function on equation image vanishing on the diagonal set and define a discontinuous additive functional by At(F) = ∑0 < stF(Xs, Xs). We establish the large deviation principle of At(F)/t by employing the Gärtner-Ellis theorem. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim