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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) = ∫Cp G(P, P′) dW(P′) and U(P) = ∫Cp dW(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 C P = ℝ2, between fields with different response functions.

Keywords

BROWNIAN FIELDSSLEPIAN'S LEMMA

Information

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

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