倒向随机微分方程弱解

提出倒向随机微分方程(简称BSDE)弱解的概念, 讨论了两类BSDE弱解存在的等价条件,并得到弱解存在的几个充分条件和减弱BSDE解存在的条件: 漂移系数g关于(y,z)满足Lipschitz 条件.     

随机微分方程终值问题的弱解(英)

设｛Wt．Ft．t∈［0．T］｝为概率空间（Ω，P）上的标准α维Brown运动，为由它生成的自然σ－代数流．本文讨论了如下随机微分方程终值问题弱解的存在性：其中ξ∈L2（Ω，P；Rn），g：［0，T」×Rn×Rnd→Rn为有界可测函数．此外，还讨论了它在金融市场期权定价问题中的应用．     

倒向随机微分方程解的Malliavin微分

讨论倒向随机微分方程Ｙｔ＝ζ＋∫＾Ｔｔｇ（ｓ,Ｙｓ,Ｚｓ）ｄｓ－∫＾ＴｔＺｓｄＷｓ解在Ｍａｌｌｉａｖｉｎ微分意义下的可微性,并得到其Ｍａｌｌｉａｖｉｎ二阶微分仍然满足一个倒向随机微分方程。用迭代方法构造一个随机序列（Ｙ＾ｎ．Ｚ＾ｎ．）,证明在Ｍａｌｌｉａｖｉｎ微分意义下二阶可微,同时证明了它在Ｓｏｂｏｌｅｖ空间Ｄ２,２则中收敛于一个线性倒向随机微分方程的解。     

随机游走和离散的倒向随机微分方程

本文研究了随机游走和离散的倒向随机微分方程。把随机游走到布朗运动的收敛推广到L^2情形；而且根据倒向随机微分方程的理论框架研究了离散的倒向随机微分方程，得到了离散的倒向随机微分方程解的存在唯一性和比较定理，这实际上给出了倒向随机微分方程的一种离散方法，为理论和实际研究提供了方便。     

第16卷B辑第3期（1995）目次和提要

第１６卷Ｂ辑第３期（１９９５）目次和提要正倒向随机微分方程的可解性和Ｈａｍｉｌｔｏｎ－Ｊ。ｏｏｂｉ—Ｂｅｌｌｍａｎ方程的零点集马进，雍炯敏本文研究一类正倒向随机含微分方程在任给时间区间上的可解性．作者设计了一个松弛随机控制们题，其中漂移项和扩散项均会...     

随机微分方程弱解的稳定性和存在性

本文研究了驱动项为无穷维Ｂｒｏｗｎ运动的一般Ｉｔ随机微分方程，给出了还问题的解和弱解的存在性关系，证明了在线性增长条件下，方程弱解的稳定性和存在性定理．     

正倒向随机微分方程的适应解及其比较定理

研究了一类正倒向随机微分方程的适应解，其中正向方程不需要满足非退化条件，我们证明了在某些单调条件下，正倒向随机微分方程存在唯一的适应解，并给出了该正倒向随机微分方程的比较定理。     

高维倒向随机微分方程比较定理

倒向随机微分方程由Pardoux和彭实戈首先提出，彭实戈给出了一维BSDE的比较定理，周海滨将其推广到了高维情形．毛学荣将倒向随机微分方程解的存在唯一性定理推广到非Lipschitz系数情况，曹志刚和严加安给了相应的一维比较定理．本文将曹志刚和严加安的比较定理推广到高维情形．     

定价问题和一类倒向随机微分方程解的存在唯一性

本文建立了由一个多维Brown运动、Poisson过程和跳时固定的简单点过程共同驱动的股票价格模型．在此模型下，将未定权益的定价问题归结为一类倒向随机微分方程的求解问题．证明了这类倒向随机微分方程适应解的存在唯一性问题，并给出了一个关于未定权益的定价公式．     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

On the convective Cahn-Hilliard equation with degenerate mobility

In this paper, we study the existence of weak solutions for the convective Cahn-Hilliard equation with degenerate mobility. Based on the Schauder type estimates, we establish the global existence of classical solutions for regularized problems. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions. The nonnegativity and the finite speed of propagation of perturbations of solutions are also discussed.     

Weak solutions to a nonlinear variational wave equation and some related problems

In this paper we present some results on the global existence of weak solutions to a nonlinear variational wave equation and some related problems. We first introduce the main tools, the L ^p Young measure theory and related compactness results, in the first section. Then we use the L ^p Young measure theory to prove the global existence of dissipative weak solutions to the asymptotic equation of the nonlinear wave equation, and comment on its relation to Camassa-Holm equations in the second section. In the third section, we prove the global existence of weak solutions to the original nonlinear wave equation under some restrictions on the wave speed. In the last section, we present global existence of renormalized solutions to two-dimensional model equations of the asymptotic equation, which is also the so-called vortex density equation arising from sup-conductivity.     

Weak solutions to the two-dimensional derivative Ginzburg-Landau equation

1.IntroductionInthepreselltpaper)westudythefollowinggeneralizedcomplexGinzburg-Landauequationintwospatialdimensions:anm=pp (1 in)au~(1 lp)Ill'"~ ox,.v(lul'u) p(x,.ac)lul',(1.1)whereallparametersarereal.Thisequation3mostlyconsideredwithor=P=0anda=1,hasalongandbroadhistoryinphysicsasagenericamplitudeequationneartheonsetofinstabilitiesinfluidmechanicalsystems,aswellasinthetheoryofphasetransitionsandsuperconductivity.Inthstspecialcase,theekistenceofsolutionsandtheirlongtimebehaviourhavebeeninves…     

Multivalued stochastic McKean-Vlasov equation

In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McKean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.     

Global weak solution for a periodic generalized Hunter–Saxton equation

In this paper, we consider a periodic generalized Hunter–Saxton equation. We obtain the existence of global weak solutions to the equation. First, we give the well-posedness result of the viscous approximate equations and establish the basic energy estimates. Then, we show that the limit of the viscous approximation solutions is a global weak solution to the equation.     

MULTIVALUED STOCHASTIC MCKEAN-VLASOV EQUATION

In this work, under global Lipschitz conditions, we prove the existence and uniqueness of strong solutions for multivalued stochastic McK ean-Vlasov equation. Moreover, under continuous and linear growth assumptions, we also obtain the existence of weak solutions.     

Existence and uniqueness of weak solutions for a non-uniformly parabolic equation

In this paper we develop a unifying method to prove the existence and uniqueness of weak solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Some well-known parabolic equations are the special cases of this equation.     

Existence and uniqueness of weak solutions for a fourth-order nonlinear parabolic equation

In this paper we establish the existence and uniqueness of weak solutions for the initial-boundary value problem of a fourth-order nonlinear parabolic equation.     

一类退化抛物方程的边值问题

In this paper, we study the boundary value problem (BVP) for a degenerate parabolic equation. By introducing a proper notion of weak solutions, we prove the uniqueness and existence of weak solutions of the problem. The localization of weak solutions is also discussed, which plays a key role in the proof of the uniqueness.     

A Nonlinear Degenerate Parabolic Equation

ＡＮｏｎｌｉｎｅａｒＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎ￥ＪｉａｎｇＹｉｎｇｊｉｅ（ＪｉａｏｚｕｏＵｎｉｖｅｒｓｉｔｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓｐａｐｅｒｗｅｓｔｕｄｙａｎｏｎｌｉｎｅｒｄｅｇｅｎｅｒａｔｅｐａｒａｂｏｌｉｃｅ...