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On the maximum of random fields represented by stochastic integrals over circles

Published online by Cambridge University Press:  14 July 2016

Enzo Orsingher
Enzo Orsingher*
Affiliation:
University of Rome
*
∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, Università di Roma ‘La Sapienza', Piazzale Aldo Moro 5, 00185 Roma, Italy.
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Abstract

In this paper we obtain an upper bound for the maximum of random fields of the form , where CP denotes circles of fixed radius and dW(P′) is a plane white noise field.

The results presented are obtained by means of successive steps involving Slepian's lemma for random fields, inequalities on Brownian fields and planar stochastic integrals.

Keywords

BROWNIAN RANDOM FIELDSSLEPIAN'S LEMMA
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 3 , September 1987 , pp. 574 - 585
Copyright
Copyright © Applied Probability Trust 1987 

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References

Adler, R. (1981) The Geometry of Random Fields. Wiley, Chichester.Google Scholar
Adler, R. (1984) The supremum of a particular Gaussian field. Ann. Prob. 12, 436–444.Google Scholar
Cabaña, E. M. (1972) On barrier problem for the vibrating string. Z. Wahrscheinlichkeitsth. 22, 13–24.Google Scholar
Cabaña, E. M. and Wschebor, M. (1981) An estimate for the tails of the distribution of the supremum for a class of stationary multiparameter Gaussian processes. J. Appl. Prob. 18, 536–541.Google Scholar
Marcus, M. B. and Shepp, L. A. (1970) Continuity of Gaussian processes. Trans. Amer. Math. Soc. 151, 377–391.Google Scholar
Orsingher, E. (1984) Damped vibrations excited by white noise. Adv. Appl. Prob. 16, 562–584.Google Scholar
Pruitt, W. E. and Orey, S. (1973) Sample functions of the N-parameter Wiener process. Ann. Prob. 1, 138–163.Google Scholar
Zimmermann, G. J. (1972) Sample functions properties of the two-parameter Gaussian processes. Ann. Math. Statist. 43, 1235–1246.Google Scholar