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Statistics of the Occupation Time of Renewal Processes
Open accessAbstract
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(26)).
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Cites
Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications
Bouchaud, J.-P., & Georges, A. (1990) · Physics Reports · doi:10.1016/0370-1573(90)90099-n · Cited by 4,162
The Theory of Stochastic Processes
Cox, D. R., Miller, H. D., Weiss, G., & Shuler, K. (1966) · Physics Today · doi:10.1063/1.3047872 · Cited by 3,324
Cited by
Metzler, R., Jeon, J.-H., Cherstvy, A. G., & Barkai, E. (2014) · Phys. Chem. Chem. Phys. · doi:10.1039/c4cp03465a · Cited by 1,765
Statistical Aging and Nonergodicity in the Fluorescence of Single Nanocrystals
Brokmann, X., Hermier, J.-P., Messin, G., Desbiolles, P., Bouchaud, J.-P., & Dahan, M. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.120601 · Cited by 391
Metadata
- Authors
- Godrèche, C., & Luck, J. M.
- Venue
- Journal of Statistical Physics
- Published
- 2001-08
- Volume
- 104
- Issue
- 3-4
- Pages
- 489-524
- ISSN
- 0022-4715 (ISSN-L)
- 1572-9613
- OpenAlex
- W1544213665
- Cited by
- 322
- References
- 2
- FWCI
- 14.06
- Type
- journal article
- Language
- en
- Open access
- green
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