 Φ-inequalities on MartingalesRuilin Long Chapter 3 in Martingale Spaces and Inequalities, 1993, pp 81-128 from Springer Abstract: Abstract The L p -inequalities introduced in the preceding chapter, concerning various operators on martingales (such as maximal operator, square operator and conditioned square operator, etc.), could be extended to so-called Φ-inequalities. In this chapter, we will study them according to Φ’s different situations: Φ is convex, or convex in a strict sense, or concave, or merely of moderate growth (we will call such Φ “general Φ” for the simplicity). §3.1 will be devoted to some elementary properties of convex functions, especially to the moderate growth property, and two related indices. §3.2–3.5 will be devoted to the general theory of Φ -inequalities in four cases, which may be useful in some domains other than martingale, then to -inequalities on martingales. The last section §3.6 will be devoted to the rearrangement technique in martingale setting. This technique is almost equivalent to “distribution” one with slight differences between them. Roughly speaking, by means of the latter, we could get general Φ-inequalities, and by means of the former we lose some generality of Φ, but as a compensation, we get better constants. In this section, we keep the assumptions imposed on (Ω, F, μ, {F n }n≥0) as before. Date: 1993 There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it. Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-322-99266-6_3 Ordering information: This item can be ordered from DOI: 10.1007/978-3-322-99266-6_3 Access Statistics for this chapter More chapters in Springer Books from Springer |
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