Recurrence properties of Processes with stationary independent increments

Let X 1 , X 2 ,…X n , … be independent and identically distributed random variables, and write . In [2] Chung and Fuchs have established necessary and sufficient conditions for the random walk {Z n } to be recurrent , i.e. for Z n to return infinitely often to every neighbourhood of the origin. The object of this paper is to obtain similar results for the corresponding process in continuous time.