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Fubini theorems giving conditions for change of the order of integration in multiple integrals are useful in all forms of calculus.
The convolution theorem is a good example of this – it makes use of switching the order of integration in a double integral.
Our new tests are wild bootstrap implementations of score-based tests for the order of integration of a fractionally integrated time series.
The choice of the order of integration (D, d) parameters is based on the plot of integrated time series and based on comparison of their standard deviation; the series having the more stabilized mean is selected.
Here, the zero result can be checked by reversing the order of integration (Fubini's Theorem) in any of the two double integrals, while leaving the other as it stands.
After the Supreme Court ratified the boycotters' victory on Dec. 17, 1956, a reporter and photographer from Look magazine asked Parks to pose for a picture illustrating the new order of integration.
where γ is an order of integration.
Changing order of integration is used in our main results.
Exchanging the order of integration, we get (11).
where we flipped the order of integration and expectation.
Exchanging the order of integration, we obtain that (3.33).
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