Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 104, Issue 3-4, Pages 489-524Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1010364003250
Keywords
occupation time; renewal processes; persistence; Brownian motion; Levy laws
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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. Godreche, and J. M. Luck((26))).
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