Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables
Conditional moments E[X 2|p|X 1 = x] of an α-stable random vector (X 1,X 2) may exist even if p ⩾ α. The precise conditions are stated in Cioczek-Georges and Taqqu _and Samorodnitsky and Taqqu . This paper provides the proof for the most delicate cases, namely 1 < α< 2 and p < 2α+ 1, which is the maximal range of possible p’s when the vector (X 1, X 2) is nondegenerate.
KeywordsCharacteristic Function Triangle Inequality Conditional Variance Integral Sign Conditional Moment
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