Probabilistic and statistical analysis of the linear fractional stable motion

In this talk we present some recent results on limit theory for high and low frequency observations of a linear fractional stable motion. The probabilistic theory contains some surprising theorems, which are non-ergodic in nature, and thus they make statistical inference more complex. Once we have demonstrated the limit theory, we will turn our attention to statistical estimation of the linear fractional stable motion, which is a three-parameter family. We show consistency and prove some associated central limit theorems for the parameter vector.