A Note on the Arc-Sine Law and Markov Random Sets
0. Introduction. The purpose of this note is to point out an extension of a theorem of Dynkin [2], [3, page 447] concerning renewal processes to the context of Markov random sets (or, as we shall call them, semilinear Markov processes). Dynkin's result states that, if X1, X2, is a "renewal sequence", i.e. a sequence of nonnegative, independent, identically distributed random variables, with partial sums Sn, and if x, is defined by