Reflections on Rice's Formulae for Level Crossings — History, Extensions and Use

Appreciation

[1]  Igor Rychlik On Some Reliability Applications of Rice's Formula for the Intensity of Level Crossings , 2000 .

[2]  J. Albin Extremes and upcrossing intensities for P-differentiable stationary processes , 2000 .

[3]  M. R. Leadbetter,et al.  Asymptotic behaviour of conditional laws and moments of (alpha)-stable random vectors, with application to upcrossing intensities , 1999 .

[4]  Gennady Samorodnitsky,et al.  Level Crossings of Absolutely Continuous Stationary Symmetric ?-stable Processes , 1997 .

[5]  D. Applebaum Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[6]  Michna Zbigniew,et al.  The expected number of level crossings for certain symmetric α-stable processes , 1995 .

[7]  R. Adler,et al.  The Expected Number of Level Crossings for Stationary, Harmonisable, Symmetric, Stable Processes , 1993 .

[8]  Michael B. Marcus,et al.  Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes , 1989 .

[9]  Correction: On the Average Number of Real Roots of a Random Algebraic Equation , 1987 .

[10]  U. Zähle A general rice formula, palm measures, and horizontal-window conditioning for random fields , 1984 .

[11]  M. R. Leadbetter,et al.  Extremes and Related Properties of Random Sequences and Processes: Springer Series in Statistics , 1983 .

[12]  Michael B. Marcus,et al.  Level Crossings of a Stochastic Process with Absolutely Continuous Sample Paths , 1977 .

[13]  Donald Geman,et al.  Occupation Times for Smooth Stationary Processes , 1973 .

[14]  David R. Brillinger,et al.  On the Number of Solutions of Systems of Random Equations , 1972 .

[15]  M. R. Leadbetter On Crossings of Levels and Curves by a Wide Class of Stochastic Processes , 1966 .

[16]  N. Ylvisaker The Expected Number of Zeros of a Stationary Gaussian Process , 1965 .

[17]  Kiyosi Itô The expected number of zeros of continuous stationary Gaussian processes , 1963 .

[18]  E. Bulinskaya On the Mean Number of Crossings of a Level by a Stationary Gaussian Process , 1961 .

[19]  V. Ivanov On the Average Number of Crossings of a Level by the Sample Functions of a Stochastic Process , 1960 .

[20]  S. Rice Mathematical analysis of random noise , 1944 .