Prove that if (X) is symmetric stable and (E|x-X|^{s}
Question:
Prove that if \(X\) is symmetric stable and \(E|x-X|^{s}<\infty\) for all \(x \in \mathbb{R}\), then as \(x ightarrow \infty(\) or \(-x ightarrow \infty)\),
\[
\frac{E|x-X|^{s}}{|x|^{s}} ightarrow 1
\]
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To prove the statement well use the definition of symmetric stable distribution and properties of ex...View the full answer
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