Statistics of the Occupation Time of Renewal Processes

By C. Godrèche, J. Luck. 2000

240 citations recorded by the source corpus.

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)).

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f8494b96acbabd7b60d7c241ed1cb3e83c98f2ef

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In Finance

1. Ralf Metzler
2. Johannes H. P. Schulz
3. Eli Barkai

In Statistics and Probability

1. Ralf Metzler
2. Johannes H. P. Schulz
3. Eli Barkai

Citations in the corpus

• Aging renewal theory and application to random walks (2013, methodology): “Moreover, despite the renewal property, the process nðtÞ is nonstationary [13]: events naðta; tÞ counted after an unattended aging period ta > 0, i.”