集值拟鞅和集值一致渐近鞅

本文讨论了集值拟鞅和集值一致渐近鞅,证明了集值拟鞅与集值一致渐近鞅的选样定理,对于集值一致渐近鞅得到了一些收敛性结果,并由此刻化了空间的 Radon-Nikodym性质.     

集值L^1—极限鞅的集值鞅逼近及其收敛性

本文证明了集值Ｌ~１－极限鞅的集值鞅逼近定理，并利用此结果以及集值鞅的收敛性结果讨论了集值Ｌ~１－极限鞅的收敛性．     

B值L^1极限鞅及其诱导集函数

设(Q,F,P)是一概率空间,Δ是一向右定向集,B是一Banach空间,(X_t,F_T,Δ)是B值L~1极限鞅,对任一,定义B值诱导集函数Q为:本文给出了定向集上B值L~1极限鞅的Riesz分解定理,讨论了它的诱导集函数的性质,并用B值L~1极限鞅及其诱导集函数刻划了B空间的Radon-Nikodym性质,一些已知的结果得到推广与改进。     

集值局部平方可积鞅

介绍集值类（D）过程和集值局部鞅的概念和有关性质，进而讨论了集值局部平方可积鞅的概念和性质。     

关于集值Pramart的某些结果

本文引进了Boohner可积函数空间L~1[Ω;X]中子集的可分解包的概念,给出了集值随机变量族本性上确界的定义及基本性质。以此为基础,研究了集值Pramart的性质;用类似于实值Snell包的方法给出了集值superpramart的上鞅逼近,证明了集值superpramart在Kuratowski-Mosco意义下的收敛定理。     

集值Pramart的一类鞅逼近

在X^＊可分的条件下,首先讨论了集值Pramart有关支撑函数和距离函数的性质,利用支撑函数和距离函数研究了集值Pramart鞅逼近,在此基础上,给出了集值Pramart的一类鞅分解.     

集值上鞅的收敛定理及 Riesz 分解

本文给出了集值鞅的进一步性质;建立了集值上鞅外穿不等式;证明了一个集值上鞅收敛定理;研究了集值上鞅的 Riesz 分解.     

集值 Pramart 的鞅分解

研究了集值Pramart的若干性质,利用支撑函数得到了集值Pramart的收敛定理,同时,证明了实值Pramart的鞅分解定理.以此为基础,给出了集值Pramart在Kuratowski-Mosco意义下的鞅分解定理.     

闭区间值鞅及模糊数值鞅

集值上鞅、下鞅和鞅的收敛定理已有不少文章进行了研究[1]、[2][3]。但在这些文章中,集值上(下)鞅并不以经典的上(下)鞅为其特款。在本文中,我们定义了以经典上(下)鞅为其特款的闭区间值上(下)鞅,并讨论了它们的性质及其收敛定理。本文还在此基础上讨论了模糊数值鞅。     

集值Superpramart的上鞅逼近

文中讨论了可积随机集条件期望的若干性质,在此基础上给出了集值Ｓｕｐｅｒｐｒａｍａｒｔ的上鞅逼近,同时,证明了集值Ｓｕｐｅｒｐｒａｍａｒｔ 在Ｋｕｒａｔｏｗｓｋｉ－Ｍｏｓｃｏ意义下的收敛定理。     

集值逆鞅的收敛性

研究集值逆鞅(集值逆上鞅)在Kuratowski收敛意义,Kuratowski-Mosco收敛意义及弱收敛意义下的收敛定理.     

Stochastic integral with respect to set-valued square integrable martingales

In this paper, we shall firstly illustrate why we should consider integral of a stochastic process with respect to a set-valued square integrable martingale. Secondly, we shall prove the representation theorem of set-valued square integrable martingale. Thirdly, we shall give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale and the representation theorem of this kind of integrals. Finally, we shall prove that the stochastic integral is a set-valued sub-martingale.     

平方可积鞅

讨论了集值平方可积鞅和实值平方可积鞅的性质.它对集值随机过程的进一步研究将起到很重要的作用.     

Martingale representation theorem for set-valued martingales

The present paper contains a martingale representation theorem for set-valued martingales defined on a filtered probability space with a filtration generated by a Brownian motion. It is proved that such type martingales can be defined by some generalized set-valued stochastic integrals with respect to a given Brownian motion. The main result of the paper is preceded by short part devoted to the definition and some properties of generalized set-valued stochastic integrals.     

On set-valued stochastic integrals in an M-type 2 Banach space

In a separable Banach space, for set-valued martingale, several equivalent conditions based on the measurable selections are discussed, and then, in an M-type 2 Banach space, at first we define single valued stochastic integral by the differential of a real valued Brownian motion, after that extend it to set-valued case. We prove that the set-valued stochastic integral becomes a set-valued submartingale, which is different from single valued case, and obtain the Castaing representation theorem for the set-valued stochastic integral, which is applicable for set-valued stochastic differential equations.     

关于集值下鞅Riesz分解的注记

在X*可分的条件下给出了集值序列及集值下鞅的一些结果,在此基础上,利用支撑函数,给出了Banach空间集值下鞅的Riesz分解定理。     

Set-valued stochastic integral equations driven by martingales

We consider a notion of set-valued stochastic Lebesgue–Stieltjes trajectory integral and a notion of set-valued stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of set-valued stochastic integral equations. The existence and uniqueness of the solution to such the equations is proven. As a generalization of set-valued case results we consider the fuzzy stochastic trajectory integrals and investigate the fuzzy stochastic integral equations driven by bounded variation processes and martingales.     

集值上鞅可Doob分解的条件

假定(X,‖·‖)为实Banach空间,X*为其对偶空间,X*可分.给出了集值上鞅几种不同的Doob分解概念,利用支撑函数研究了集值上鞅在各种分解意义下可Doob分解的充分必要条件.     

Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization

In this paper we introduce a class of set-valued increasing-along-rays maps and present some properties of set-valued increasing-along-rays maps. We show that the increasing-along-rays property of a set-valued map is close related to the corresponding set-valued star-shaped optimization. By means of increasing-along-rays property, we investigate stability and well-posedness of set-valued star-shaped optimization.