The Statistical Inference for Generalized Stable Processes

By using the Itô calculus, the maximum likelihood estimators of the paramaters of generalized stable processes based on the information, on a given time interval 0, t, of the jumps of size greater than or equal to ε are proved to be strongly consistent not only as t tends to infinity, while ε is fixed, but also as ε tends to 0 and t is fixed. Moreover, we also prove that the convergent rates fit the law of the iterated logarithm for the strongly consistent estimators.