Occupation time statistics of the random acceleration model
| Autor: | Boutcheng, Hermann Joel Ouandji, Bouetou, Thomas Bouetou, Burkhardt, Theodore W., Rosso, Alberto, Zoia, Andrea, Crepin, Kofane Timoleon |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are non-trivial and not yet completely understood. In this paper we consider the occupation time $T_+$ of the one-dimensional random acceleration model on the positive half-axis. We calculate the first two moments of $T_+$ analytically and also study the statistics of $T_+$ with Monte Carlo simulations. One goal of our work was to ascertain whether the occupation time $T_+$ and the time $T_m$ at which the maximum of the process is attained are statistically equivalent. For regular Brownian motion the distributions of $T_+$ and $T_m$ coincide and are given by L\'evy's arcsine law. We show that for randomly accelerated motion the distributions of $T_+$ and $T_m$ are quite similar but not identical. This conclusion follows from the exact results for the moments of the distributions and is also consistent with our Monte Carlo simulations. Comment: 10 pages, 4 figures |
| Databáze: | arXiv |
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