On Probability and Moment Inequalities for Supermartingales and Martingales

On Probability and Moment Inequalities for Supermartingales and Martingales

Burkholder's type inequality is stated for the special class of martingales, namely the product of independent random variables. The constants in the latter are much less than in the general case which is considered in Nagaev (Acta Appl. Math. 79, 35-46, 2003; Teor. Veroyatn. i Primenen. 51(2),...

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Veröffentlicht in:Acta applicandae mathematicae 2007-07, Vol.97 (1-3), p.151-162
1. Verfasser: Nagaev, S V
Format: Artikel
Sprache:eng
Schlagworte:
Constants
Independent variables
Inequalities
Inequality
Martingales
Mathematical models
Mathematics
Probability
Random variables
Studies
Theory
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Zusammenfassung:Burkholder's type inequality is stated for the special class of martingales, namely the product of independent random variables. The constants in the latter are much less than in the general case which is considered in Nagaev (Acta Appl. Math. 79, 35-46, 2003; Teor. Veroyatn. i Primenen. 51(2), 391-400, 2006). On the other hand, the moment inequality is proved, which extends these by Wittle (Teor. Veroyatn. i Primenen. 5(3), 331-334, 1960) and Dharmadhikari and Jogdeo (Ann. Math. Stat. 40(4), 1506-1508, 1969) to martingales.
ISSN:0167-8019
1572-9036
DOI:10.1007/s10440-007-9131-0