2026-04-17T18:43:41Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1959252025-12-04T20:47:25Zcom_2072_1057col_2072_478822col_2072_478917

00925njm 22002777a 4500 dc Masoliver, Jaume, 1951- author Palassini, Matteo author 2023-03-24T11:47:51Z 2023-03-24T11:47:51Z 2023-02-10 2023-03-24T11:47:51Z 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. Processos estocàstics Processos de moviment brownià Stochastic processes Brownian motion processes Counting of level crossings for inertial random processes: Generalization of the Rice formula