双指标非交换鞅的收敛性和不等式

本文研究了双指标非交换鞅的收敛性和不等式问题.利用非交换代数和单指标鞅的方法,获得了双指标Lp-有界鞅(1≤p≤∞)的收敛性,L1-收敛性和一致可积的关系;推广了双指标非交换鞅的两个不等式,即Burkholder-Gundy不等式和强鞅的Davis不等式.     

鞅的加权Ф-不等式

本文研究了鞅空间的极大算子和极小算子。利用鞅方法。得到了关于鞅的强型和弱型加权Ф-不等式的一个必要条件．     

鞅的加权Φ-不等式

本文研究了鞅空间的极大算子和极小算子,利用鞅方法,得到了关于鞅的强型和弱型加权Φ-不等式的一个必要条件.     

鞅的Ф-原子分解与鞅的凹Ф-不等式

引入了鞅的三种类型Ф-原子概念，建立了HФ，FФ，DФ鞅空间的Ф-原子分解定理，利用Ф-原子分解方法证明了一些鞅的凹Ф-不等式．     

双指标非交换鞅的一些不等式

本文研究了双指标非交换鞅的一些不等式问题.利用单指标非交换鞅不等式的方法,获得了双指标非交换鞅的||·||H_p(M)和||·||h_p(M)之间的关系(2≤p∞).推广了双指标非交换鞅的||·||L_p(M)和||·||h_p(M)之间的等价关系(2≤p≤4).     

Banach空间向量值Bochner积分型的广义Jensen不等式

一维空间R中的Jensen不等式在概率论与鞅论等学科中都有着广泛的应用.本文以锥为工具,将这个著名的不等式推广到序Banach空间,得出向量值的Bochner积分型的广义Jensen不等式.     

一类风险过程的Lundberg不等式

本文研究了保费收入是复合Poisson过程,而理赔含有多个相关险种的风险过程,利用鞅方法,给出了这种推广情形下的Lundberg 不等式,从而可以估计相应的破产概率.     

马氏调制费率下复合Poisson风险模型的Lundberg型不等式

对于具有马氏调制费率的复合Poisson风险模型，用无穷小生成元构造鞅的方法，导出了破产概率的Lundberg不等式。     

一类带干扰索赔相关风险模型的破产概率

讨论一类带干扰索赔相关且保费收取为一复合泊松过程风险模型的破产问题，利用鞅方法得出Lundberg不等式和最终破产概率公式。     

相关随机利率下的双二项模型的破产概率

研究带有相关随机利率的双二项风险模型,得到了破产概率的积分表达式,并利用鞅分析的方法得到了破产概率的经典Lundberg上界,另外给出了一个破产概率的比经典Lundberg上界更精确的上界.     

GENERALIZED ROSENTHAL'S INEQUALITY FOR BANACH-SPACE-VALUED MARTINGALES

A generalized Rosenthal's inequality for Banach-space-valued martingales is proved, which extends the corresponding results in the previous literatures and character-izes the p-uniform smoothness and q-uniform convexity of the underlying Banach space. As an application of this inequality, the strong law of large numbers for Banach-space-valued martingales is also given.     

局部平方可积鞅的比值不等式

本对局部平方可积鞅建立了几个比值不等式，推广了连续鞅的相应结果．     

局部平方可积鞅的比值不等式

本文对局部平方可积鞅建立了几个比值不等式,推广了连续鞅的相应结果.     

Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions

We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given.      

Weak type inequality for noncommutative differentially subordinated martingales

In the paper we focus on self-adjoint noncommutative martingales. We provide an extension of the notion of differential subordination, which is due to Burkholder in the commutative case. Then we show that there is a noncommutative analogue of the Burkholder method of proving martingale inequalities, which allows us to establish the weak type (1,1) inequality for differentially subordinated martingales. Moreover, a related sharp maximal weak type (1,1) inequality is proved. Research supported by MEN Grant 1 PO3A 012 29.     

Two parameter smooth martingales on the Wiener space

We prove that two parameter smooth continuous martingales have ∞-modification and establish a Doob's inequality in terms of (p, r)-capacity for two parameter smooth martingales.     

Some new results for demimartingales

Harremoёs obtained some new maximal inequalities for non-negative martingales. In this paper, we get some new maximal and minimal inequalities for non-negative demimartingales which generalize the results of Harremoёs. We also obtain an inequality for non-negative demimartingales which generalizes the result of Iksanov and Marynych. Finally we obtain a strong law of large numbers, strong growth rate and integrability of supremum for demimartingales which generalize and improve the result of Chow.     

Burkholder-Gundy-Davis inequality in martingale Hardy spaces with variable exponent

In this article, by extending classical Dellacherie's theorem on stochastic sequences to variable exponent spaces, we prove that the famous Burkholder-Gundy-Davis inequality holds for martingales in variable exponent Hardy spaces. We also obtain the variable exponent analogues of several martingale inequalities in classical theory, including convexity lemma, Chevalier's inequality and the equivalence of two kinds of martingale spaces with predictable control. Moreover, under the regular condition on σ-algebra sequence we prove the equivalence between five kinds of variable exponent martingale Hardy spaces.     

Clarkson不等式与Banach空间几何

我们证明了Banach空间X是Clarkson p型（q余型）当且仅当X是一个特殊的p一致光滑空间（q-一致凸空间（）,我们还找到刻划型（余型）的一系列鞅不等式,同时,我们得到了均方函数sharp不等式。     

The Umd Constants of the Summation Operators

The UMD property of a Banach space is one of the most useful properties when one thinks about possible applications. This is in particular due to the boundedness of the vector-valued Hilbert transform for functions with values in such a space. Looking at operators instead of at spaces, it is easy to check that the summation operator does not have the UMD property. The actual asymptotic behavior however of the UMD constants computed with martingales of length n is unknown. We explain, why it would be important to know this behavior, rephrase the problem of finding these UMD constants and give some evidence of how they behave asymptotically.