共查询到20条相似文献,搜索用时 15 毫秒
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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
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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
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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
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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
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本文主要研究了一类多项Caputo分数阶随机微分方程的Euler-Maruyama (EM)方法,并证明了其强收敛性.具体地,我们首先构造了求解多项Caputo分数阶随机微分方程初值问题的EM方法,然后证明分数阶导数的指标满足$\frac{1}{2}<\alpha_{1}<\alpha_{2}<\cdots<\alpha_{m}<1$时,该方法是$\alpha_{m}-\alpha_{m-1}$阶强收敛的.文末的数值试验验证了理论结果的正确性. 相似文献
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李娟 《数学物理学报(B辑英文版)》2006,26(3):443-450
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations (FBSDEs) with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations (BSDEs) with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions. 相似文献
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本文讨论Euler方法用于求解线性中立型随机延迟微分方程初值问题时数值解的稳定性,利用了一种不同于以往文献中的证明技巧,给出了Euler方法均方稳定的一个充分条件.文末的数值试验证实了本文所获理论结果的正确性. 相似文献
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Hu Lanying Ren Yong 《Annals of Differential Equations》2007,23(4):416-421
In this paper,we derive the continuous dependence on the terminal condition of solutions to nonlinear reflected backward stochastic differential equations involving the subdifferential operator of a lower semi-continuous,proper and convex function under non-Lipschitz condition by means of the corollary of Bihari inequality. 相似文献
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本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂(CEMS)方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果. 相似文献
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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
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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
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In this paper,by constructing proper Lyapunov functions,exponential stability criteria for stochastic delay partial differential equations are obtained. An example is shown to illustrate the results. 相似文献
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吴臻 《数学物理学报(B辑英文版)》2004,24(1):91-99
The existence and uniqueness results of fully coupled forward-backward stochastic differential equations with stopping time (unbounded) is obtained. One kind of comparison theorem for this kind of equations is also proved. 相似文献
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Wei Zhang 《计算数学(英文版)》2020,38(6):903-932
The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with
Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under
the local Lipschitz condition plus Khasminskii-type condition. We also study its strong
convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are
given to illustrate the theoretical results. 相似文献