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- W2069087438 abstract "Exact comparisons are made relating E|Y0|p, E|Yn−1|p, and E(maxj≤n−1 |Yj|p), valid for all martingales Y0,…,Yn−1, for each p ≥ 1. Specifically, for p > 1, the set of ordered triples {(x, y, z) : x = E|Y0|p, y = E |Yn−1|p, and z = E(maxj≤n−1 |Yj|p) for some martingale Y0,…,Yn−1} is precisely the set {(x, y, z) : 0≤x≤y≤z≤Ψn,p(x, y)}, where Ψn,p(x, y) = xψn,p(yx) if x > 0, and = an−1,py if x = 0; here ψn,p is a specific recursively defined function. The result yields families of sharp inequalities, such as E(maxj≤n−1 |Yj|p) + ψn,p∗(a) E |Y0|p ≤ aE |Yn−1|p, valid for all martingales Y0,…,Yn−1, where ψn,p∗ is the concave conjugate function of ψn,p. Both the finite sequence and infinite sequence cases are developed. Proofs utilize moment theory, induction, conjugate function theory, and functional equation analysis." @default.
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- W2069087438 date "1986-04-01" @default.
- W2069087438 modified "2023-09-24" @default.
- W2069087438 title "Prophet regions and sharp inequalities for pth absolute moments of martingales" @default.
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- W2069087438 doi "https://doi.org/10.1016/0047-259x(86)90072-2" @default.
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