一种新型二次变差

证明了基于停线的局部平方可积强鞅的二次变差的存在性,得到了重要的Ｂｕｒｋｈｏｌｄｅｒ－Ｄａｖｉｓ－Ｇｕｎｄｙ不等式。     

两指标局部鞅的停止变换及Wiener过程的鞅刻划

本文主要讨论两指标局部平方可积鞅的停止变换问题及Ｗｉｅｎｅｒ过程的鞅刻划和停止问题。     

局部平方可积鞅的Chung重对数律(英文)

设X＝（Xt，t0）为局部平方可积鞅，且Xo＝0，＜X，X＞t为其二阶可料变差．利用连续半鞅的强逼近结果，我们证明了在较弱的条件下，X的Chung重对数律成立，即     

多指标随机积分的局部性质

设 M,是 n 指标平方可积鞅,φ∈L~2(d<(?)>),φ∈L~2(d<>),W-(?)本文证明了随机积分的三个局部性质:对F∈(?),L是停面,G=(?),Γ=(?)是随机区间形的可料集,那么1.1_FM=1_F(?),1_(Fφ)=1_(F(?))(?)1_FW=1_F(?),2.1_GM=1_G(?),1_(Gφ)=1_(G(?))(?)1_GW=1_G(?),3.1_rΔ(?)M=1_rΔ(?)(?),1_(rφ)=1_(r(?))(?)1_(?)W=1_rΔ(?)(?).     

关于局部平方可积鞅的重对数律

设(M_t,f_t,t≥0)为(Ω,f,P)上的局部平方可积鞅,(简记M ∈m_100~2),M_=0,{f_t}满足通常条件,f_0={Φ,Ω},为M~2的可料补偿,本文证明了如下结论: ⅰ)若存在可料过程k_t t≥0,k_t=0 a.s.,使得 |△M_t|≤k_t·_t~(1/2)/[2lg_2 k~2V_t)]~(1/2) a.s.,_∞=∞, 则 M_t/[2_t lg_2(e~2V_t)]~(1/2)=1 a.s. ⅱ)若存在可料过程K_t,t≥0和常数0_t~(1/2)/[21g_2(e~2V_t)]~(1/2) a.s. 则存在0<8(K)<1,↓8(K)=0,使在_∞=∞上, M_t/[2_t lg_2(e~2V_t)]~(1/2)≤1 8(K) a.s.     

Strong approximation of locally square-integrable martingales

In this paper, we consider the strong approximation for locally square-integrable martingales. In our results, the limit process may be a process with jumps. This is an extension of the former results.     

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．     

平方协变差和连续半鞅的推广Ito^公式

令X是连续半鞅，f是R上的局部可积函数。本文我们将证明，只要∫0tf(Xs)ds存在，那么平方协变差存在且等于-∫Rf(a)daLta,Lat是X的局部时。因此对具有导数f的绝对连续函数F，有推广的Ito^公式F（Xt)=F(X0) ∫0tf(Xs)dXs 1/2[f(X),X]t。     

Y（F4‘）条件与加强形式的停止定理

首次提出了Ｙ（Ｆ４＇）条件，给出了Ｙ（Ｆ４＇）条件的两个等价关系，得到了加强形式的停止定理和强鞅的一个等价关系。     

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。     

Stochastic integration for operator valued processes on hilbert spaces and on nuclear spaces

The representation of a nuclear space valued square integrable martingale by means of another nuclear space valued square integrable martingale is given in terms of stochastic inegrals of operator valued processes. The construction of the stochastic integral goes through that of operator valued processes on Hilbert spaces. A new approach is given for the Hilbertian case, so that only the integration of Hilbert-Schmidt operator valued processes is needed to represent square integrable martingales     

Laws of the iterated logarithm for locally square integrable martingales

Three types of laws of the iterated logarithm （LIL） for locally square integrable martingales with continuous parameter are considered by a discretization approach. By this approach, a lower bound of LIL and a number of FLIL are obtained, and Chung LIL is extended.     

股票操作选时的最优停止问题

股票操作中的选时即决定何时买进何时卖出是人们进行操作时最为关心的,本文运用最优停止及时间序更的理论和方法,给出了一种较优的具体操作方法。     

有界可料过程关于集值平方可积鞅的集值随机积分

本文定义了一类有界可料过程关于集值平方可积鞅的集值随机积分,并研究了集植随机积分的性质。此为建立集值随机分析的理论奠定了基础。     

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.     

Strong Markov Properties for Markov Random Fields

Markov properties and strong Markov properties for random fields are defined and discussed. Special attention is given to those defined by I. V. Evstigneev. The strong Markov nature of Markov random fields with respect to random domains such as [0, L], where L is a multidimensional extension of a stopping time, is explored. A special case of this extension is shown to generalize a result of Merzbach and Nualart for point processes. As an additional example, Evstigneev's Markov and strong Markov properties are considered for independent increment jump processes.