scholarly journals Asymptotic behavior of some oscillatory integrals

1979 ◽  
Vol 31 (1) ◽  
pp. 127-140
Author(s):  
Hitoshi KITADA
Keyword(s):  
Asymptotic Behavior ◽  
Oscillatory Integrals

scholarly journals Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization

2018 ◽  
Vol 38 (2) ◽  
pp. 271-286 ◽  
Author(s):  
Ivan Nourdin ◽  
Atef Lechiheb ◽  
Guangqu Zheng ◽  
Ezzedine Haouala
Keyword(s):  
Asymptotic Behavior ◽  
Long Range ◽  
Elliptic Equations ◽  
Random Coefficients ◽  
Oscillatory Integrals ◽  
Long Range Dependence ◽  
Stochastic Integrals ◽  
Highly Oscillatory

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 onedimensional elliptic equations with highly oscillatory random coefficients displaying long-range dependence, by proving convergence to stochastic integrals with respect to Hermite processes.

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