Asymptotic Theory of Weakly Dependent Random Processes by Emmanuel Rio

Author:Emmanuel Rio
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

where

Remark 6.2

We refer to Appendix C for more about the quantities involved in these moment inequalities. Note that Q can be replaced by in Theorem 6.3.

Proof

As in the proof of Theorems 6.1 and 6.2 we may assume that for any . Under this assumption . First,

Now, applying Theorem 6.2 with , we get that

(6.20)

with

We now bound . Since H is the right-continuous inverse of R, if and only if . Hence, interchanging the integrals, we obtain that

(6.21)

To bound , we introduce the change of variable . Then

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