Statistics of the occupation time of renewal processes

Details Statistics of the occupation time of renewal processes Statistics of the occupation time of renewal processes

2000-10-26

arxiv.org/abs/cond-mat/0010428v1

Journal of Statistical Physics 104 (2001), 489-524.

Physics

Condensed Matter

Statistical Mechanics

32 pages, latex

Scientific paper

We present a systematic study of the statistics of the occupation time and related random variables for stochastic processes with independent intervals of time. According to the nature of the distribution of time intervals, the probability density functions of these random variables have very different scalings in time. We analyze successively the cases where this distribution is narrow, where it is broad with index $\theta <1$, and finally where it is broad with index $1<\theta <2$. The methods introduced in this work provide a basis for the investigation of the statistics of the occupation time of more complex stochastic processes (see joint paper by G. De Smedt, C. Godr\`{e}che, and J.M. Luck).

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