ON LEVEL CROSSINGS AND CYCLES IN DAM PROCESSES.

The classical dam with input according to a process with stationary, independent increments and output at unit rate is considered. The stochastic properties of level crossings, i. e. , up- and downcrossings, of a fixed level x greater than 0 are studied. It is shown that successive downcrossings of any such level constitute a renewal process with a. s. strictly positive lifetimes. This property allows the content process to be described as a regenerative process. In fact several types of imbedded renewal processes may be defined and various cycles in the content process may be identified.