共查询到20条相似文献,搜索用时 9 毫秒
1.
In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth. 相似文献
2.
3.
本文讨论Hilert空间中非线性随机微分-积分方程解的存在性,唯一性,在我们所 一组条件下,得到了解的局部存在唯一性的结果。 相似文献
4.
TANG Shanjian 《数学年刊B辑(英文版)》2005,26(3):437-456
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs. The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions. 相似文献
5.
TANG Shanjian 《数学年刊B辑(英文版)》2005,26(3):437-456
This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions. 相似文献
6.
RELATIONS BETWEEN SOLUTIONS TO STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SEMIMARTINGALE WITH NON-LIPSCHITZ COEFFICIENTS 总被引:1,自引:0,他引:1
Weiyin Fei School of Math. Physics Anhui University of Technology Science Wuhu Anhui 《Annals of Differential Equations》2010,(1):16-23
In this paper, a class of stochastic differential equations (SDEs) driven by semi-martingale with non-Lipschitz coefficients is studied. We investigate the dependence of solutions to SDEs on the initial value. To obtain a continuous version, we impose the conditions on the local characteristic of semimartingale. In this case, it gives rise to a flow of homeomorphisms if the local characteristic is compactly supported. 相似文献
7.
In this paper,we obtain the stability of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd),under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition by means of the corollary of Bihari inequality. 相似文献
8.
EXISTENCE AND MOMENT ESTIMATES FOR SOLUTIONS TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS
Daoyi Xu Bing Li Shujun Long Lingying Teng Weisong Zhou 《Annals of Differential Equations》2014,(1):62-84
In this paper, we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients. Some moment estima- tes of the solutions are given by establishing new Ito operator inequalities based on the Razumikhin technique. These estimates improve, extend and unify some related results including exponential stability of Mao (1997) [20], decay stability of Wu et al. (2010,2011) [32,33], Pavlovic et al. (2012) [24], asymptotic behavior of Luo et al. (2011) [18] and Song et al. (2013) [26]. Moreover, stochastic version of Wintner theorem in continuous space is established by the comparison principle, which improve and extend the main results of Xu et al. (2008 [39], 2013 [36]). When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces, we extend the related results of Govindana et al. (2013) [7], Liu et al. (2007) [15], Vinod- kumar (2010) [29] and Xu et al. (2012) [35]. Two examples are provided to illustrate the effectiveness of our results. 相似文献
9.
首先,针对一类线性倒向随机微分方程,给出了g-鞅同鞅之间相互联系所满足的充分条件.通过该条件得到了经典的Black-Scholes模型下未定权益的公平价格过程以及最优增长投资策略的价格过程.其次,引入了带惩罚的非线性倒向随机微分方程,并通过惩罚比率的不同取值来讨论相关的经济学意义. 相似文献
10.
《Annals of Differential Equations》2012,(3):283-289
By applying the properties of almost periodic function and exponential dichotomy of linear system as well as Banach fixed point theorem,we establish the conditions for the existence and uniqueness of square-mean almost periodic solution to some stochastic functional differential equations. 相似文献
11.
Shouying Huang Yanhong Zhang College of Math. Computer Science Fuzhou University Fuzhou 《Annals of Differential Equations》2011,(4):440-449
In this paper we study solutions to a forward Dynamo equation depending continuously on the velocity on an exterior domain,using Logarithmic Convexity Methods.We obtain some more weaker conditions by introducing the unbounded domain. 相似文献
12.
13.
14.
15.
论文首先证明了非线性随机分数阶微分方程解的存在唯一性,然后构造了数值求解该方程的Euler方法,并证明了当方程满足一定约束条件时,该方法是弱收敛的.特别地,当分数阶α=0时,该方程退化为非线性随机微分方程,所获结论与现有文献中的相关结论是一致的;当α≠0,且初值条件为齐次时,所获结论可视为现有文献中线性随机分数阶微分方... 相似文献
16.
高凌云 《数学物理学报(B辑英文版)》2010,30(3):932-938
We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations. 相似文献
17.
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. 相似文献
18.
本文讨论一般非线性随机延迟微分方程Heun方法的数值稳定性,证明了如果问题本身满足零解是均方指数稳定和均方渐近稳定的充分条件,则当方程的漂移项进一步满足一定的条件时,Heun方法是Ms.稳定的,带线性插值的Heun方法是均方指数稳定的和GMS-稳定的理论结果.文末的数值试验进一步验证了所得的相关结论. 相似文献
19.
In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role. 相似文献
20.
高凌云 《数学物理学报(B辑英文版)》2002,22(4)
Using Nevanlinna theory of the value distribution of meromorphic functions, the author investigates the problem of the growth of solutions of two types of algebraic differential equation and obtains some results. 相似文献