A Maximal inequality of non-negative submartingale. Issue 3 (1999)

• Record Type: Journal Article
• Authors: Kim, Young-Ho
• Is Part Of: Journal of inequalities and applications. Volume 3:Issue 3(1999)
• Page Start: 285
• Page End: 291
• Publication Date: 1999
• Subjects: Maximal inequality; Submartingale; Strongly subordinate; Inner product; Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/S1025583499000193
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : In this paper, we prove the maximal inequalityλ P ( sup n ≥ 0 ( f n + | g n | ≥ λ ) ≤ ( Q ( 1 ) + 2 ) | | f | | 1, λ > 0, between a non-negative submartingalef, g is strongly subordinate tof and1 − 2 f n − 1 − Q ( 1 ) ≤ 0, whereQ is real valued function such that0 < Q ( s ) ≤ s for eachs > 0, Q ( 0 ) = 0 . This inequality improves Burkholder's inequality in whichQ ( 1 ) = 1 .