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Counting of level crossings for inertial random processes: Generalization of the Rice formula by Masoliver, Jaume; Palassini, Matteo is a scholarly article available to read on EtoBox.

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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.

Author

Masoliver, Jaume; Palassini, Matteo

Published

2023

Language

EN