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On the comparison of the distribution of the supremum of random fields represented by stochastic integrals

Published online by Cambridge University Press:  01 July 2016

Enzo Orsingher  and
Bruno Bassan
Enzo Orsingher*
Affiliation:
University of Salerno
Bruno Bassan*
Affiliation:
University of Rome ‘La Sapienza'
*
∗Postal address: Dipartimento di Informatica e Applicazioni, University of Salerno, 84100, Italy.
∗∗Postal address: Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome ‘La Sapienza', Piazzale Aldo Moro 5, 00185 Roma, Italy.
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Abstract

In this paper we compare the distribution of the supremum of the Gaussian random fields Z(P) = ∫CpG(P, P′) dW(P′) and U(P) = ∫CpdW(P'), where CP are circles of fixed radius, dW is a white noise field and G are special deterministic response functions.

The results obtained permit us to establish upper bounds for the distribution of the supremum of Z(P) by applying some well-known inequalities on U(P).

The comparison of the suprema is carried out also, when CP = ℝ2, between fields with different response functions.

Keywords

BROWNIAN FIELDSSLEPIAN'S LEMMA
Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 4 , December 1989 , pp. 770 - 780
Copyright
Copyright © Applied Probability Trust 1989 

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References

[1] Adler, R. J. (1981) The Geometry of Random Fields. Wiley, Chichester.Google Scholar
[2] Adler, R. J. (1984) The supremum of a particular Gaussian field. Ann. Prob. 12, 436–444.Google Scholar
[3] Bowman, F. (1958) Introduction to Bessel Functions. Dover, New York.Google Scholar
[4] 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
[5] Gradshteyn, I. S. and Ryzhik, I. M. (1980) Table of Integrals, Series and Products. Academic Press, New York.Google Scholar
[6] Orsingher, E. (1987) On the maximum of random fields represented by stochastic integrals over circles. J. Appl. Prob. 24, 574–585.Google Scholar
[7] Yadrenko, M. I. (1983) Spectral Theory of Random Fields. Optimization Software Inc., Publications Division, New York.Google Scholar