Kac-Rice formula: A contemporary overview of the main results and applications

Berzin, Corinne; Latour, Alain; León, J. B.

doi:10.48550/arxiv.2205.08742

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Appendix B: Simulation Methods1

Introduction1

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2023

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“…( 26) after using Eqs. (20) and (23). As in Brownian motion the resulting expression is clumsy and we will not write it explicitly.…”

Section: Appendix B: Simulation Methodsmentioning

confidence: 99%

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Counting of level crossings for inertial random processes: Generalization of the Rice formula

Masoliver

Palassini²

2023

Phys. Rev. E

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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.

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“…( 26) after using Eqs. (20) and (23). As in Brownian motion the resulting expression is clumsy and we will not write it explicitly.…”

Section: Appendix B: Simulation Methodsmentioning

confidence: 99%

“…Moreover, extensions to the counting of critical points were also obtained. For rigorous recent reviews of these developments, we refer to the books [22,23]. In this work, we will only be concerned with one-dimendional random processes (d = d = 1).…”

Section: Introductionmentioning

confidence: 99%

Counting of level crossings for inertial random processes: Generalization of the Rice formula

Masoliver

Palassini²

2023

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

Kac-Rice formula: A contemporary overview of the main results and applications

Cited by 1 publication

References 40 publications

Counting of level crossings for inertial random processes: Generalization of the Rice formula

Counting of level crossings for inertial random processes: Generalization of the Rice formula

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