Department of Condensed Matter Physics and Institute of Complex Systems (UBICS) University of Barcelona, 08028 Barcelona, Catalonia, Spain.
Phys Rev E. 2023 Feb;107(2-1):024111. doi: 10.1103/PhysRevE.107.024111.
We address the counting of level crossings for inertial stochastic processes. We review Rice's approach to the problem and generalize the classical Rice formula to include all Gaussian processes in their most general form. We apply the results to some second-order (i.e., inertial) processes of physical interest, such as Brownian motion, random acceleration and noisy harmonic oscillators. For all models we obtain the exact crossing intensities and discuss their long- and short-time dependence. We illustrate these results with numerical simulations.
我们研究了惯性随机过程的穿越计数问题。我们回顾了 Rice 对这个问题的研究方法，并将经典的 Rice 公式推广到了最一般的形式，包括所有的高斯过程。我们将这些结果应用于一些具有物理意义的二阶（即惯性）过程，如布朗运动、随机加速度和噪声谐振子。对于所有模型，我们都得到了精确的穿越强度，并讨论了它们的长时和短时依赖性。我们通过数值模拟来说明这些结果。
