The variation of a stable path is stable

Summary Let X(t) be a separable symmetric stable process of index . Let P be a finite partition of [0,1], and a collection of partitions. The variation of a path X(t) is defined in three ways in terms of the sum collection . Under certain conditions on and on the parameters and , the distribution of the variation is shown to be a stable law. Under other conditions the distribution of the variational sum converges to a stable distribution.The author wishes to thank Prof. J. Chover for several helpful suggestions.