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 characterizes 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.

DOUBLE Φ-INEQUALITIES FOR BANACH-SPACE-VALUED MARTINGALES

Let B be a Banach space, φ1, φ2 be two generalized convex φ-functions and φ1, φ2 the Young complementary functions of ψ1, ψ2 respectively with∫t t0ψ2（s）/sds≤ds≤c0ψ1（c0t）（t〉t0）for some constants co 〉 0 and to 〉 0, where ψ1 and ψ2 are the left-continuous derivative functions of ψ1 and ψ2, respectively. We claim that： （i） If B is isomorphic to a p-uniformly smooth space （or q-uniformly convex space, respectively）, then there exists a constant c 〉 0 such that for any B-valued martingale f = （fn）n≥0,｜｜f^＊｜｜φ1≤｜｜S^（p）（f）｜｜φ2（of｜｜S^（q）（f）｜｜φ1≤c｜｜f^＊｜｜φ2,respectively）,where f^＊ and S^（p） （f） are the maximal function and the p-variation function of f respectively; （ii） If B is a UMD space, Tvf is the martingale transform of f with respect to v = （Vn）z≥0 （V^＊ 〈 1）, then ｜｜（Tvf）^＊｜｜Ф1≤f^＊｜｜Ф2.

Atomic decompositions of Banach-space-valued martingales

Several theorems for atomic decompositions of Banach-space-valued martingales are proved. As their applications, the relationship among some martingale spaces such asH α(X) andρ H α in the case 0< α? are studied. It is shown that there is a close connection between the results and the smoothness and convexity of the value spaces.

TRANSFORMS, DIFFERENTIAL SUBORDINATIONS AND A_p-WEIGHTED INEQUALITIES FOR BANACH-SPACE-VALUED REGULAR MARTINGALES

In this paper we proved the A(p)-weighted inequalities for martingale transforms and differential subordinations of Banach-space-valued regular maringales. We discussed the relations between the weighted inequalities, A(p)-weight functions and the Banach spaces which has the UMD property or are isomorphic to Hilbert space.

NEW DOOB'S MAXIMAL INEQUALITIES FOR MARTINGALES

Let 1≤q≤∞,b be a slowly varying function and letΦ:[0,∞)■[0,∞)be an increasing convex function withΦ(0)=0 and■Φ(r)=∞.In this paper,we present a new class of Doob’s maximal inequality on Orlicz-Lorentz-Karamata spaces LΦ,q,b.The results are new,even for the Lorentz-Karamata spaces withΦ(t)=tp,the Orlicz-Lorentz spaces with b≡1,and weak Orlicz-Karamata spaces with q=∞in the framework of LΦ,q,b-Moreover,we obtain some even stronger qualitative results that can remove the△2-condition of Liu,Hou and Wang(Sci China Math,2010,53(4):905-916).

Application of martingale theory in enterprise investment decision making

From the point of view of the basic option model, enterprise investment decision making under uncertainty is studied based on the martingale method. The study shows that investment options and yields are increasing functions of time, and when the option equals the yield, the investment opportunity cost is the least, which is the appropriate time for the enterprise investment. Under the condition that the investment yield is an increasing function of time, the investment opportunity cost is also an increasing function of time after the time when the investment option equals the investment yield. So the investors should invest as soon as possible, otherwise they should stop investment forever in this project. It is impossible to acquire more investment yields by indefinitely delaying the investment. Meanwhile, the study also shows that the martingale method, used widely in financial investment theory, is a powerful tool for enterprise investment decision making.

Upper Bounds for the L_p-norms of the Maximal Functions of Martingales

Let 2≤p【∞ and let (f n) be a martingale. Using exponential bounds of the probabilities of the type P(|f n|】λ‖T(f n)‖ ∞) for some quasi-linear operators acting on martingales, we estimate upper bounds for the L p-norms of the maximal functions of martinglaes. Our result is the extension and improvements of the results obtained previously by HITCZENKO and ZENG .

数理模型下抵押贷款共同保险的Martingale评价

假设未偿付额可由风险信用评估得到,房产价格服从一般Ito过程,构建了抵押贷款共同保险的数理评价模型,利用Martingale评价方法,得到了房屋抵押贷款共同保险的精确定价公式。

Martingale在控制论中的应用

本文用工程界熟悉的语言阐述鞅(Martingale)的含义以及鞅论(包括随机积分和随机微分方程——随机分析)在系统辨识、自适应控制、随机控制与滤波中的应用.从而说明,鞅论是现代控制理论中一个重要工具,应该引起工程界的足够的重视.

住房抵押贷款限额保险的Martingale评价

引入期权定价理论,利用鞅定价方法,得到了房屋抵押贷款限额保险的精确定价公式,其中未偿付额为常数,房产价格服从一般ITO过程。

随机利率下住房抵押贷款保险的创新及Martingale评价

在住房抵押贷款部分担保保证险的基础上进行了创新设计,并引入期权定价理论,利用鞅定价方法,分析了随机利率模型下该抵押贷款保险的定价问题,得到了该抵押贷款保险的无套利定价公式,其中房价服从一般扩散过程.Vasic?e kIto?

跳扩散模型下住房抵押贷款限额保险的Martingale评价

利用特殊的鞅定价方法,得到了住房抵押贷款限额保险的定价公式,其中假设房价服从Merton跳扩散过程。

LORENTZ MARTINGALE SPACES AND INTERPOLATION

In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.

ATOMIC DECOATOMIC DECOMPOSITIONS AND DUALS OF WEAK HARDY SPACES OF B-VALUED MARTINGALES

In this article, several weak Hardy spaces of Banach-space-valued martingales are introduced, some atomic decomposition theorems for them are established and their duals are investigated. The results closely depend on the geometrical properties of the Banach space in which the martingales take values.

TWO-WEIGHT WEAK-TYPE MAXIMAL INEQUALITIES FOR MARTINGALES

In this article, some necessary and sufficient conditions are shown in order that the inequality of the form Ф1（λ）Pu（f^＊〉λ）≤Ev （Ф2（C｜f∞｜）） holds with some constant C 〉 0 independent of martingale f = （fn）n≥0 and λ 〉 0, where Фl and Ф2 are a pair of Young functions, f^＊=sup n≥0｜fn｜ adn f∞=lim n→∞ fn a.e.

Two-Parameter Banach Space Valued Strong Martingales and Characterizations of p-Smoothable Spaces

In this paper we introduce the concept of two-parameterB-valued strong martingales and investigate some features of these strong martingales. We also characterizep-smoothable Banach spaces in terms of these strong martingales.

INTERPOLATION OF LORENTZ-ORLICZ MARTINGALE SPACES

In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.

CONVERGENCE OF WEIGHTED AVERAGES OF MARTINGALES IN NONCOMMUTATIVE BANACH FUNCTION SPACES

Let x （xn）≥1 be a martingale on a noncommutative probability space n （M, r） and （wn）n≥1 a sequence of positive numbers such that Wn = ∑ k=1^n wk →∞ as n →∞ We prove that x = （x.）n≥1 converges in E（M） if and only if （σn（x）n≥1 converges in E（.hd）, where E（A//） is a noncommutative rearrangement invariant Banach function space with the Fatou property and σn（x） is given by σn（x） = 1/Wn ∑k=1^n wkxk, n=1, 2, .If in addition, E（Ad） has absolutely continuous norm, then, （an（x））≥1 converges in E（.M） if and only if x = （Xn）n≥1 is uniformly integrable and its limit in measure topology x∞∈ E（M）.

THE MINIMAL OPERATOR AND WEIGHTED INEQUALITIES FOR MARTINGALES

In this article the authors introduce the minimal operator on martingale spaces, discuss some one-weight and two-weight inequalities for the minimal operator and characterize the conditions which make the inequalities hold.

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.