Asymptotic behavior of mean uniform norms for sequences of Gaussian processes and fields

Extremes

Volumn 8, Issue 3, 2005, Pages 161-169

  Seleznjev, Oleg ^a,b  

^a UMEÅ UNIVERSITY   (Sweden)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Extreme values; Gaussian field; Gaussian process; Uniform norm

Indexed keywords

EID: 33748329714     PISSN: 13861999     EISSN: 1572915X     Source Type: Journal    
DOI: 10.1007/s10687-006-7965-x     Document Type: Article

References (17)

1. Buslaev, A.P., Seleznjev, O.: On certain extremal problems in approximation theory of random processes. East J. Approx. 5, 467-481 (1999)
2. Cramér, H., Leadbetter, M.R.: Stationary and Stochastic Processes. Wiley, New York (1967)
3. Cressie, N.A.C.: Statistics for Spatial Data. Wiley, New York (1993)
4. Eplett, W.T.: Approximation theory for simulation of continuous Gaussian processes. Probab. Theory Relat. Fields 73, 159-181 (1986)
5. Feinerman, R.P., Newman, D.J.: Polynomial Approximation, Williams and Wilkins. Baltimore, (1974)
6. Hüsler, J., Piterbarg, V., Seleznjev, O.: On convergence of the uniform norms for Gaussian processes and linear approximation problems. Ann. Appl. Probab. 13, 1615-1653, (2003)
7. Leadbetter, M.R., Lindgren, G., Rootzén, H.: Extremes and Related Properties of Random Sequences and Processes. Springer, Berlin Heidelberg New York (1983)
8. Lifshits, M.: Gaussian Random Functions. Kluwer, Dordrecht (1995)
9. ∞-norm with respect to r-fold Wiener measure. J. Approx. Theory 84, 31-40 (1996)
10. Müller-Gronbach, T., Ritter, K.: Uniform reconstruction of Gaussian processes. Stoch. Processes Appl. 69, 55-70 (1997)
11. Pickands, J. III.: Upcrossing probabilities for stationary Gaussian processes. Trans. Amer. Math. Soc. 145, 51-73 (1969)
12. Piterbarg, V.: Asymptotic Methods in the Theory of Gaussian Processes and Fields. AMS, Rhode Island (1996)
13. Ritter, K.: Average Case Analysis of Numerical Problems. Lecture Notes in Math 1733. Springer, Berlin Heidelberg New York (1999)
14. Seleznjev, O.: Limit theorems for maxima and crossings of a sequence of Gaussian processes and approximation of random processes. J. Appl. Prob. 28, 17-32 (1991)
15. Seleznjev, O.: Linear approximation of random processes and sampling design problems. In: Grigelionis, B., Kubilius, J., Paulauskas, V., Pragarauskas H., Statulevicius, V., (eds.) Prob. Theory and Math. Statistics, Proceed, of the 7th Vilnius Conf. and 23th European Meet. Stat. VSP/TEV, Netherlands, pp. 665-684 (1999)
16. Seleznjev, O.: Spline approximation of random processes and design problems. J. Stat. Plan. Inference 84, 249-262 (2000)
17. Wahba, G.: Spline Models for Observational Data. SIAM, Philadelphia (1990)