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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 38, Fasc. 2,
pages 271 - 286
DOI: 10.19195/0208-4147.38.2.2
 

CONVERGENCE OF RANDOM OSCILLATORY INTEGRALS IN THE PRESENCE OF LONG-RANGE DEPENDENCE AND APPLICATION TO HOMOGENIZATION

Atef Lechiheb
Ivan Nourdin
Guangqu Zheng
Ezzedine Haouala

Abstract: This paper deals with the asymptotic behavior of random oscillatory integrals in the presence of long-range dependence. As a byproduct, we solve the corrector problem in random homogenization of one-dimensional elliptic equations with highly oscillatory random coefficients displaying long-range dependence, by proving convergence to stochastic integrals with respect to Hermite processes.

2010 AMS Mathematics Subject Classification: Primary: 60F05, 80M40; Secondary: 60H05, 60H20, 60G10, 60G18.

Keywords and phrases: Elliptic equation, Hermite process, oscillatory integral, corrector, homogenization.

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