Abstract
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 [4]_and Samorodnitsky and Taqqu [12]. 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.
This research was supported by the ONR grant N00014-90-J-1287 and NSF grants DMS-9404093 and NCR-9404931 at Boston University.
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Cioczek-Georges, R., Taqqu, M.S. (1998). Sufficient Conditions for the Existence of Conditional Moments of Stable Random Variables. In: Karatzas, I., Rajput, B.S., Taqqu, M.S. (eds) Stochastic Processes and Related Topics. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-2030-5_4
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DOI: https://doi.org/10.1007/978-1-4612-2030-5_4
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