Statistics of the occupation time of renewal processes

We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent interval s of time. According to the nature of the distribution of time intervals, t he probability density functions of these random variables have very differ ent scalings in time. We analyze successively the cases where this distribu tion is narrow, where it is broad with index theta < 1, and finally where i t is broad with index 1 < theta < 2. The methods introduced in this work pr ovide a basis for the investigation of the statistics of the occupation tim e of more complex stochastic processes (see joint paper by G. De Smedt, C. Godreche, and J. M. Luck((26))).