Mathematical Foundations of Time Series Analysis by Jan Beran

Author:Jan Beran
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

and, for d ≥ 0,

Remark 6.10

implies

so that

Problem 6.9

Solution 6.9

Follows from properties of the gamma function and in particular Stirling’s formula.

Lemma 6.21

Assumption:

Then

Proof

Then

and

imply

Stirling’s formula

implies, for x 1, x 2 →∞ with x 1/x 2 → c (0 < c < ∞),

For

we have

and hence

Finally,

so that

Corollary 6.14

Assumptions:

Then

Moreover, for λ ≠ 0,

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