On Probability and Moment Inequalities for Supermartingales and Martingales

• Autores: S. V. Nagaev
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 97, Nº. 1-3, 2007, págs. 151-162
• Idioma: inglés
• DOI: 10.1007/s10440-007-9131-0
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• Resumen

  • 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.