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.     

B值拟鞅不等式及其应用

本文给出B值拟鞅的概率不等式与集合不等式,并用它们刻划了B空间的p可光滑性及q可凸性,作为应用,还证明了B值拟鞅的强大数律,收敛速度及极大值函数的可积性。     

Quadratic variation of martingales in Riesz spaces

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austin?s sample function theorem, on convergence of the quadratic variation processes of martingales.     

Clifford鞅的b+p-权不等式及其应用

如果Cl,S是一个Clifford代数,v是一个非负测度,ψ是一个Cl,S-值可测函数,那么dμ=ψdv是一个Cl,S-值测度.在这篇论文中将证明如果ψ满足某些b+p-权条件那么关于测度dμ的Clifford-值鞅的一些不等式成立,且应用这些不等式在权ψ∈b+∞∩a1时获得了一些关于Clifford-值鞅的权对偶空间.     

Maximal inequalities for demimartingales and a strong law of large numbers

Chow's maximal inequality for (sub)martingales is extended to the case of demi(sub)martingales introduced by Newman and Wright (Z. Wahrsch. Verw. Geb. 59 (1982) 361–371). This result serves as a “source” inequality for other inequalities such as the Hajek–Renyi inequality and Doob's maximal inequality and leads to a strong law of large numbers. The partial sum of mean zero associated random variables is a demimartingale. Therefore, maximal inequalities and a strong law of large numbers are obtained for associated random variables as special cases.     

Weak type inequalities for vector-valued martingales

We obtain weak versions of the Burkholder–Davis–Gundy inequalities for vector-valued martingales by employing the operator-valued martingale transform technique. These inequalities are closely related to the geometric properties of the underlying Banach space.     

复空间的凸性与Hardy鞅不等式

本文研究了取值于复拟Banach空间的一种特殊类型的鞅——Hardy鞅的不等式与该空间的解析一致凸性的关系,证明了Hardy鞅的q均方函数的弱(1,1)型,强(p,p)型和凸φ函数的不等式,并应用它们给出了复空间的解析q一致可凸性的等价条件.同时借助于复平面单位圆中的Banach空间值解析函数和Brown运动给出了同样的刻划.     

Interpolation and Φ-moment inequalities of noncommutative martingales

This paper is devoted to the study of Φ-moment inequalities for noncommutative martingales. In particular, we prove the noncommutative Φ-moment analogues of martingale transformations, Stein’s inequalities, Khintchine’s inequalities for Rademacher’s random variables, and Burkholder–Gundy’s inequalities. The key ingredient is a noncommutative version of Marcinkiewicz type interpolation theorem for Orlicz spaces which we establish in this paper.     

Semi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma,and applications to local times

With the help of the Garsia-Rodemich-Rumsey lemma, some improvements of the Burkholder-Davis-Gundy inequalities for continuous martingales are obtained, as well as certain estimates of the L^p norm of the supremum of (a) the local times of a continuous semi-martingale and (b) the difference of the local times of two continuous martingales.     

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.     

具有AUMD性质的复Banach空间的某些特征

本应用解析鞅的一类特殊的不等式给出了具有AUMD性质的复Banach空间的某些特征。     

Two extensions of asymptotic methods in controlled Markov chains

The application of the Skorokhod representation of martingales and of the local asymptotic normality to derive limit inequalities for the cost in controlled finite state Markov chains is reviewed. The inequalities are usable in self-optimizing control. The methods are taken from the references listed but, with the exception of proposition 4, the results are formulated for Markov chains for the first time.     

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.     

Distributional inequalities for noncommutative martingales

We establish distributional estimates for noncommutative martingales, in the sense of decreasing rearrangements of the spectra of unbounded operators, which generalises the study of distributions of random variables. Our results include distributional versions of the noncommutative Stein, dual Doob, martingale transform and Burkholder-Gundy inequalities. Our proof relies upon new and powerful extrapolation theorems. As an application, we obtain some new martingale inequalities in symmetric quasi-Banach operator spaces and some interesting endpoint estimates. Our main approach demonstrates a method to build the noncommutative and classical probabilistic inequalities in an entirely operator theoretic way.     

复拟Banach空间的PL一致光滑性及其鞅刻划

本文引进了空间的ＰＬ一致光滑性与复对称鞅，证明了等价赋范定理，得到了一系列关于ＰＬ一致光滑空间的复对称鞅不等式，并应用复对称鞅的大数定律给出了值空间的ＰＬ一致光滑性的刻划。     

Concentration inequalities and laws of large numbers under epistemic and regular irrelevance

his paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance that are expressed using lower and upper expectations. The results build upon De Cooman and Miranda’s recent inequalities and laws of large numbers. The proofs indicate connections between the theory of martingales and concepts of epistemic and regular irrelevance.     

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。     

Weak martingale Hardy spaces and weak atomic decompositions

In this paper we define some weak martingale Hardy spaces and three kinds of weak atoms. They are the counterparts of martingale Hardy spaces and atoms in the classical martingale Hp-theory. And then three atomic decomposition theorems for martingales in weak martingale Hardy spaces are proved. With the help of the weak atomic decompositions of martingale, a sufficient condition for a sublinear operator defined on the weak martingale Hardy spaces to be bounded is given. Using the sufficient condition, we obtain a series of martingale inequalities with respect to the weak Lp-norm, the inequalities of weak (p ,p)-type and some continuous imbedding relationships between various weak martingale Hardy spaces. These inequalities are the weak versions of the basic inequalities in the classical martingale Hp-theory.     

Inequalities for random fields

This paper gives extensions of the Doob and Burkholder inequalities for certain classes of random fields. The Brennan-Doob inequality for V-quasimartingales is extended to the case p > 1 and is shown to hold for the class of decomposable processes satisfying the Doob inequality of Wong and Zakai [10]. A Doob inequality for the class of i-martingales having finite quadratic variation in the non-martingale coordinate is shown. For the class of quasi martingales having independent increments two Burkholder-type inequalities are derived