Occupation time statistics of the random acceleration model

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 figure

Q-Band Millimeter-Wave Antennas: An Enabling Technology for MultiGigabit Wireless Backhaul

[EN] The bandwidth demands in mobile communication systems are growing exponentially day by day as the number of users has increased drastically over the last five years. This mobile data explosion, together with the fixed service limitations, requires a new approach to support this increase in bandwidth demand. Solutions based on lower-frequency microwave wireless systems may be able to meet the bandwidth demand in a short term. However, with the small-cell mass deployment requiring total capacities of 1 Gb/s/km2, scalable, multigigabit backhaul systems are required. Millimeter-wave technology fits nicely into these new backhaul scenarios as it provides extended bandwidth for high-capacity links and adaptive throughput rate, which allows efficient and flexible deployment. Besides these advantages, millimeter-wave solutions become even more attractive when the cost of backhaul solutions and the cost of spectrum licenses are factored in. Compared to the cost of laying fiber to a cell base station, which is the only other scalable solution, the millimeter-wave solution becomes the most appropriate approach.The research leading to these results received funding from the European Commission's seventh Framework Programme under grant agreement 288267.Vilar Mateo, R.; Czarny, R.; Lee, ML.; Loiseaux, B.; Sypek, M.; Makowski, M.; Martel, C.... (2014). Q-Band Millimeter-Wave Antennas: An Enabling Technology for MultiGigabit Wireless Backhaul. IEEE Microwave Magazine. 15(4):121-130. https://doi.org/10.1109/MMM.2014.2308769S12113015