Please use this identifier to cite or link to this item:
https://scholarbank.nus.edu.sg/handle/10635/104154
DC Field | Value | |
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dc.title | Some best possible prophet inequalities for convex functions of sums of independent variates and unordered martingale difference sequences | |
dc.contributor.author | Choi, K.P. | |
dc.contributor.author | Klass, M.J. | |
dc.date.accessioned | 2014-10-28T02:45:55Z | |
dc.date.available | 2014-10-28T02:45:55Z | |
dc.date.issued | 1997-04 | |
dc.identifier.citation | Choi, K.P.,Klass, M.J. (1997-04). Some best possible prophet inequalities for convex functions of sums of independent variates and unordered martingale difference sequences. Annals of Probability 25 (2) : 803-811. ScholarBank@NUS Repository. | |
dc.identifier.issn | 00911798 | |
dc.identifier.uri | http://scholarbank.nus.edu.sg/handle/10635/104154 | |
dc.description.abstract | Let Φ(·) be a nondecreasing convex function on [0, ∞). We show that for any integer n ≥ 1 and real a, EΦ((Mn - a)+) ≤ 2EΦ((Sn - a)+) - Φ(0) and E(Mn ∨ med Sn) ≤ E|Sn -med Sn|. where X1, X2, . . . are any independent mean zero random variables with partial sums S0 = 0, Sk = X1 + . . . + Xk and partial sum maxima Mn = max0≤k≤nSk. There are various instances in which these inequalities are best possible for fixed n and/or as n → ∞. These inequalities remain valid if {Xk} is a martingale difference sequence such that E(Xk | {Xi: i ≠ k}) = 0 a.s. for each k ≥ 1. Modified versions of these inequalities hold if the variates have arbitrary means but are independent. | |
dc.source | Scopus | |
dc.subject | Convex function | |
dc.subject | Maximum of partial sums | |
dc.subject | Median | |
dc.subject | Prophet inequalities | |
dc.subject | Sums of independent random variables | |
dc.subject | Unordered martingale difference sequence | |
dc.type | Article | |
dc.contributor.department | MATHEMATICS | |
dc.description.sourcetitle | Annals of Probability | |
dc.description.volume | 25 | |
dc.description.issue | 2 | |
dc.description.page | 803-811 | |
dc.identifier.isiut | NOT_IN_WOS | |
Appears in Collections: | Staff Publications |
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