Level crossings of absolutely continuous stationary symmetric α-stable processes

Annals of Applied Probability

Volumn 7, Issue 2, 1997, Pages 460-493

  Adler, Robert ^a,b   Samorodnitsky, Gennady ^c  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b University of North Carolina at Chapel Hill   (United States)

^c Cornell University   (United States)

Author keywords

Level crossings; Stable processes

Indexed keywords

EID: 0031138898     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

1. ADLER, R., SAMORODNITSKY, G. and GADRICH, T. (1993). The expected number of level crossings for stationary, harmonizable, symmetric, stable processes. Ann. Appl. Probab. 3 553-575.
2. BRILLINGER, D. R. (1972). On the number of solutions of systems of random equations. Ann. Math. Statist. 43 534-540.
3. p-radonifying operators. Ann. Probab. 13 885-897.
4. CIOCZEK-GEORGES, R. and TAQQU, M. S. (1994). How do conditional moments of stable vectors depend on the spectral measure? Stochastic Process. Appl. 54 95-112.
5. CIOCZEK-GEORGES, R. and TAQQU, M. S. (1995). Necessary conditions for the existence of conditional moments of stable random variables. Stochastic Process. Appl. 56 233-246.
6. CRAMÉR, H. and LEADBETTER, M. R. (1967). Stationary and Related Stochastic Processes. Wiley, New York.
7. GEMAN, D. and HOROWITZ, J. (1973). Occupation times for smooth stationary processes. Ann. Probab. 1 131-137.
8. HAUSER, R. and MATZINGER, H. (1995). Conditional distributions of stable vectors. Unpublished manuscript.
9. LEADBETTER, M. R., LINDGREN, G. and ROOTZÉN, H. (1983). Extremes and Related Properties of Random Sequences and Processes. Springer, New York.
10. LEDOUX, M. and TALAGRAND, M. (1991). Probability in Banach Spaces: Isoperimetry and Processes. Springer, New York.
11. MARCUS, M. B. (1977). Level crossings of a stochastic process with absolutely continuous sample paths. Ann. Probab. 5 52-71.
12. MARCUS, M. B. (1989). Some bounds for the expected number of level crossings of symmetric harmonizable p-stable processes. Stochastic Process. Appl. 33 217-231.
13. MARUYAMA, G. (1970). Infinitely divisible processes. Theory Probab. Appl. 15 1-22.
14. MICHNA, Z. and RYCHLIK, I. (1992). Characteristics of upcrossings for stable processes. Technical report, Dept. Mathematical Statistics, Lund Institute of Technology.
15. MICHNA, Z. and RYCHLIK, I. (1992). Expected number of level crossings for certain symmetric α-stable processes. Comm. Statist. - Stochastic Models 11 1-19.
16. RICE, S. O. (1945). Mathematical analysis of random noise. Bell System Tech. J. 24 46-156.
17. ROSIŃSKI, J. (1986). On stochastic integral representation of stable processes with sample paths in Banach spaces. J. Multivariate Anal. 20 277-302.
18. ROSIŃSKI, J. (1995). On the structure of stationary stable processes. Ann. Probab. 23 1163-1187.
19. SAMORODNITSKY, G. and TAQQU, M. S. (1994). Stable Non-Gaussian Random Processes. Chapman and Hall, New York.