Ornstein—Uhlenbeck过程的重点问题

本文主要讨论了单参数ｄ维Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程的重点的存在性和多重时的Ｈａｕｓｄｏｒｆｆ维数，得到了：当ｄ≤３时，以正概率样本轨道具有两重点，且两重时具有Ｈａｕｓｄｏｒｆｆ维数２－ｄ２；当ｄ≤２时，以正概率样本轨道具有三重点，且三重时具有Ｈａｕｓｄｏｒｆｆ维数３－ｄ。     

分支特征为ψ(x,λ)=γ(x)λ~(1 β)超布朗运动的击中概率(英文)

本文研究了分支特征为 ψ( x,λ) =γ( x) λ1 β( 0 <β≤ 1 )的超布朗运动 ,给出了这类超过程关于球内及球外区域的击中概率     

两参数Ornstein－Uhlenbeck过程的连续模

对［２］中引入的两参数Ｏｒｎｓｔｅｉｎ－Ｕｈｌｅｎｂｅｃｋ过程Ｘ（ｕ，ｖ），如果我们定义增量△ｕ，ｓ（ｖ）＝｜Ｘ（ｕ＋ｘ，ｖ）－Ｘ（ｕ，ｖ）｜，则我们可以找到正则化因子βｖ，使得若，则若，则这里     

一类广泛超稳定过程占位时的渐近行为

本文在「１」的基础上，针对非常值分枝率对应的一类广泛超α－稳定过程占位时过程，证明了在非临界情况下其渐近行为与「１」中相同，但在临界时其渐近性依赖于分枝率在无穷远点的极限行为，从而得到了更为精细的结果。     

催化介质中的超Ornstein-Uhlenbeck 过程

本文构造了催化介质中的Ornstein-Uhlenbeck过程,并在有限测试情形,证明了其persistence性质（d=1)。     

Fleming—Viot测度值过程

ＦＶ－超过程是测度值过程研究的重要内容之一，近两年有较大的发展，本文系统地介绍了有关的知识，并对其研究的方法及存在的问题进行了简单的讨论。     

一类具有临界状态的Athreya—Karlin BPRE.灭种概率的渐近行为

当随机环境为一有限状态平遍成Ｍａｒｋｏｖ链时，本文证明了总存在常数ｃ１，ｃ２〉０，使得一类含有临界状态的上临界Ａｔｈｒｅｙａ－Ｋａｒｌｉｎ ＢＰＲＥ随初始众数Ｋ无限增大时相应的灭种概率ｑｋ的负对数的变化恒介于ｃ１ｌｏｇｋ与ｃ２ｋ之间。     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE SYSTEM OF ONE-DIMENSIONAL NONLINEAR THERMOVISCOELASTICITY

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｉｓｐａｐｅｒｉｓｄｅｖｏｔｅｄｔｏｔｈｅｓｔｕｄｙｏｆｔｈｅｌａｒｇｅｔｉｍｅｂｅｈａｖｉｏｕｒｏｆｓｍｏｏｔｈｓｏｌｕｔｉｏｎｓｆｏｒｉｎｉｔｉａｌｂｏｕｎｄａｒｙｖａｌｕｅｐｒｏｂｌｅｍｓｉｎｏｎｅｄｉ...     

QUASI-STATIONARY DISTRIBUTIONS FOR THE RADIAL ORNSTEIN-UHLENBECK PROCESSES

The purpose of this article is to obtain the quasi-stationary distributions of the δ（δ 〈 2）-dimensional radial Ornstein-Uhlenbeck process with parameter -λ by using the methods of Martinez and San Martin （2001）. It is described that the law of this process conditioned on first hitting 0 is just the probability measure induced by a （4 - δ）- dimensional radial Ornstein-Uhlenbeck process with parameter -λ. Moreover, it is shown that the law of the conditioned process associated with the left eigenfunction of the process conditioned on first hitting 0 is induced by a one-parameter diffusion.     

具有两参数的非线性椭圆型方程边值问题解的渐近性态

讨论一类具有双参数的非线性椭圆型方程边值问题. 引入多重尺度变量, 构造问题的形式渐近解. 利用微分不等式理论, 证明边值问题渐近解的存在性和一致有效性. 由解的结构指出, 在两参数一定的情况下,相应问题的解只具有一个边界层.     

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary.     

THE ASYMPTOTIC BEHAVIOR OF SOLUTION FOR A CLASS OF STRONGLY NONLINEAR NON-AUTONOMOUS EQUATION

In this paper, using the singularly perturbed theory and the boundary layer corrective method, the asymptotic behavior of solution for a class of strongly nonlinear non-autonomous equations and the infection for asymptotic behavior of the solution with regard to the boundary condition are studied. According to the different regions of the boundary value, the asymptotic expansions of the solution for the original problem are obtained simply and conveniently.     

ASYMPTOTIC BEHAVIOR TOWARD THERAREFACTION WAVE FOR SOLUTIONS OFRATE-TYPE VISCOELASTIC SYSTEM WITH BOUNDARY EFFECT

1IntroductionWeconsiderthefollowinginitialboundaryvalueproblemonR =(o, oo)forarate-typeviscoelasticsystemwiththeinitial-boundaryconditionsWherev5uand-pdenotethestrain,partialvelocityandstressrespectively,whileEisapositiveconstant,whichrepresentthedynamicYoung'smodulus,andT>Oisarelaxationtime.Forsimplicity,weassumeT=1.PR(v)standsfortheequilibriumvalueforp-Theinitialdata(vo,bolpo)(x)areassumedtotendtotheconstantstate,asx- oowherep =pR(v )sincepR(v)istheequilibriumvaluef0rp.M0reover,thecompa…     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR DELAY DIFFERENTIAL EQUATIONS

Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved.     

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATION

The boundedness of the every solution and the asymptotic behavior of all solutions of the nonlinear neutral delay differential equation [x(t) - P(t)x(t - t)]' Q1 (t)f(x{t-σ1))-Q2(t)f(x(t -σ2))=0,t≥t0 are investigated, whereτ,σ1,σ2∈(0,∞), P∈C([t0,∞),R), and Q1,Q2∈C([t0,∞),R), f∈C(R,R). The sufficient conditions obtained improve the existing results in the literatures.