论文信息 - Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes

Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes

Some bounds for the expected number of crossings of a level by a real valued symmetric harmonizable p-stable process defined on the interval [0, T] are obtained. Most of the results are analogous to the well known results for stationary Gaussian processes.

Michael B. Marcus | M. Marcus

[1] X. Fernique. Regularite des trajectoires des fonctions aleatoires gaussiennes , 1975 .

[2] G. Pisier,et al. Random Fourier Series with Applications to Harmonic Analysis. , 1981 .

[3] G. Pisier,et al. Characterizations of almost surely continuousp-stable random Fourier series and strongly stationary processes , 1984 .

[4] Kiyosi Itô,et al. On the convergence of sums of independent Banach space valued random variables , 1968 .

[5] M. Marcus. ξ-radial processes and random Fourier series , 1987 .

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

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

[8] R. Dudley. The Sizes of Compact Subsets of Hilbert Space and Continuity of Gaussian Processes , 1967 .

[9] N. Ylvisaker. On a Theorem of Cramer and Leadbetter , 1966 .

[10] M. Talagrand. Regularity of gaussian processes , 1987 .

[11] harald Cramer,et al. Stationary And Related Stochastic Processes , 1967 .