Statistics of the occupation time of renewal processes

2000/10/26 by C. Godreche, J. M. Luck · 2 citations
Physics and Astronomy · #cond-mat.stat-mech

paper · pdf

published as Journal of Statistical Physics 104 (2001), 489-524. · 32 pages, latex

arxiv created 2000/10/26 · arxiv updated 2009/11/30

Abstract

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 θ<1, and finally where it is broad with index 1<θ<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. Godrèche, and J.M. Luck).

Cited by

• Nonlinear Response Relations and Fluctuation-Response Inequalities for Nonequilibrium Stochastic Systems
• Statistical properties of stochastic functionals under general resetting

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