Moment Inequality for the Martingale Square Function

• Autorzy: Adam Osękowski
• Języki publikacji: EN

Abstrakty

EN

Consider the sequence $(Cₙ)_{n≥1}$ of positive numbers defined by C₁ = 1 and $C_{n+1} = 1 + Cₙ²/4$, n = 1,2,.... Let M be a real-valued martingale and let S(M) denote its square function. We establish the bound
𝔼 |Mₙ|≤ Cₙ𝔼 Sₙ(M), n=1,2,...,
and show that for each n, the constant Cₙ is the best possible.

Kategorie tematyczne

• 60G42: Martingales with discrete parameter
• 60E15: Inequalities; stochastic orderings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2013
• Tom: 61
• Numer: 2
• Strony: 169-180

Daty

wydano

2013

Twórcy

autor

Adam Osękowski

• Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland

Identyfikatory

DOI

10.4064/ba61-2-11