Laws of the iterated logarithm of Chover-type for operator stable Lévy processes

Let X={X(t),t∈R+} be an operator stable Lévy process in Rd with exponent E, where E is an invertible linear operator on Rd. Integral tests for sample paths of operator stable Lévy process X are given. Laws of the iterated logarithm of Chover-type are derived from them as corollaries. Our results give information about the maximal growth rate of sample paths of X in terms of the real parts of the eigenvalues of E.