Some estimates related to the Doob’s martingale inequalities

2019 ◽  
Vol 153 ◽  
pp. 124-129
Author(s):  
Milica Jovalekić
Keyword(s):  
Martingale Inequalities

New variable martingale Hardy spaces

2021 ◽  
pp. 1-29
Author(s):  
Yong Jiao ◽  
Dan Zeng ◽  
Dejian Zhou
Keyword(s):  
Brownian Motion ◽  
Hardy Space ◽  
Hardy Spaces ◽  
Stochastic Integral ◽  
Lebesgue Spaces ◽  
Type Space ◽  
Variable Lebesgue Spaces ◽  
Martingale Inequalities

We investigate various variable martingale Hardy spaces corresponding to variable Lebesgue spaces $\mathcal {L}_{p(\cdot )}$ defined by rearrangement functions. In particular, we show that the dual of martingale variable Hardy space $\mathcal {H}_{p(\cdot )}^{s}$ with $0<p_{-}\leq p_{+}\leq 1$ can be described as a BMO-type space and establish martingale inequalities among these martingale Hardy spaces. Furthermore, we give an application of martingale inequalities in stochastic integral with Brownian motion.

scholarly journals Noncommutative weak Orlicz spaces and martingale inequalities

2011 ◽  
Vol 204 (3) ◽  
pp. 195-212 ◽  
Author(s):  
Turdebek N. Bekjan ◽  
Zeqian Chen ◽  
Peide Liu ◽  
Yong Jiao
Keyword(s):  
Orlicz Spaces ◽  
Martingale Inequalities

Martingales

2021 ◽  
pp. 313-343
Author(s):  
James Davidson
Keyword(s):  
Martingale Theory ◽  
Basic Properties ◽  
Martingale Inequalities ◽  
Martingale Convergence ◽  
Doob Decomposition

This chapter summarizes the essentials of sequential conditioning and martingale theory. After a review with examples of the basic properties of martingales and semi‐martingales, including the Doob decomposition, the upcrossing inequality and martingale convergence are studied and also the role of the conditional variances in establishing convergence. The important martingale inequalities of Kolmogorov, Doob, Burkholder, and Azuma are proved.

A New Characterization of Hardy Martingale Cotype Space

2004 ◽  
Vol 47 (4) ◽  
pp. 481-491
Author(s):  
Turdebek N. Bekjan
Keyword(s):  
Banach Space ◽  
Best Constants ◽  
Plurisubharmonic Functions ◽  
Martingale Inequalities ◽  
Martingale Cotype

AbstractWe give a new characterization of Hardy martingale cotype property of complex quasi- Banach space by using the existence of a kind of plurisubharmonic functions. We also characterize the best constants of Hardy martingale inequalities with values in the complex quasi-Banach space.

scholarly journals Martingale inequalities of type Dzhaparidze and van Zanten

Statistics ◽  
2017 ◽  
Vol 51 (6) ◽  
pp. 1200-1213 ◽  
Author(s):  
Xiequan Fan ◽  
Ion Grama ◽  
Quansheng Liu
Keyword(s):  
Martingale Inequalities

scholarly journals Non-Commutative Martingale Inequalities

1997 ◽  
Vol 189 (3) ◽  
pp. 667-698 ◽  
Author(s):  
Gilles Pisier ◽  
Quanhua Xu
Keyword(s):  
Martingale Inequalities

scholarly journals A NECESSARY AND SUFFICIENT CONDITION FOR CERTAIN MARTINGALE INEQUALITIES IN BANACH FUNCTION SPACES

2007 ◽  
Vol 49 (3) ◽  
pp. 431-447 ◽  
Author(s):  
MASATO KIKUCHI
Keyword(s):  
Function Space ◽  
Probability Space ◽  
Banach Function Space ◽  
Sufficient Conditions ◽  
Function Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Banach Function Spaces ◽  
Martingale Inequalities ◽  
Necessary And Sufficient

AbstractLet X be a Banach function space over a nonatomic probability space. We investigate certain martingale inequalities in X that generalize those studied by A. M. Garsia. We give necessary and sufficient conditions on X for the inequalities to be valid.

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