Systems of quasilinear parabolic equations in Rn and systems of quadratic backward stochastic differential equations
Systems of quasilinear parabolic equations in Rn and systems of quadratic backward stochastic differential equations
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Rn 中的拟线性抛物型方程组和二次向后随机微分方程组
DOI：
10.1016/j.matpur.2021.01.006
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Yam, Sheung Chi
中科院分区：
文献类型：
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作者：
Bensoussan, Alain;Frehse, Jens;Yam, Sheung Chi
本文的目的有两个方面。第一个目标是完成Bensoussan和Frehse [2]以前的工作。本文的一个很大的局限性是它们是偏微分方程系统。在一个有界域上人们可以期望解是有界的，因为人们寻找光滑解。这对于方法的发展是非常重要的性质。这也是真的，存在于有界域的解决方案可能不存在于R n，因为缺乏边界。本文给出了文献[2]的结果推广到Rn的条件.第二个目标是考虑偏微分方程系统的倒向随机微分方程（Bundle）形式。这是Xing和Z Ziitković最近工作的目标[8]。他们认为系统的二次增长，这是一个著名的开放问题的Bethesda文献。由于Bu是马尔可夫的，所以这个问题等价于解析问题。然而，由于这种动机的分析问题是在R n，而不是在一个有界域。Xing和Z Zhitković开发了一种概率方法。分析问题和Besides之间的联系并不明显。我们的目标是表明，分析方法可以完全转化为一个概率。然而，概率概念在转化为分析框架之后也是有用的。对于唯一性结果尤其如此。
The objective of this paper is two-fold. The first objective is to complete the former work of Bensoussan and Frehse [2]. One big limitation of this paper was the fact that they are systems of PDE. on a bounded domain. One can expect solutions to be bounded, since one looks for smooth solutions. This is a very important property for the development of the method. It is true also that solutions which exist in a bounded domain may fail to exist on R n, because of the lack of bounds. We give conditions so that the results of [2] can be extended to R n. The second objective is to consider the BSDE (Backward stochastic differential equations) version of the system of PDE. This is the objective of a more recent work of Xing and Z̆itković [8]. They consider systems of BSDE with quadratic growth, which is a well-known open problem in the BSDE literature. Since the BSDE are Markovian, the problem is equivalent to the analytic one. However, because of this motivation the analytic problem is in R n and not on a bounded domain. Xing and Z̆itković developed a probabilistic approach. The connection between the analytic problem and the BSDE is not apparent. Our objective is to show that the analytic approach can be completely translated into a probabilistic one. Nevertheless probabilistic concepts are also useful, after their conversion into the analytic framework. This is in particular true for the uniqueness result.
DOI：
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发表时间：
2002
期刊：
影响因子：
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作者：
A. Bensoussan;J. Frehse
通讯作者：
J. Frehse
对角椭圆系统的评论
DOI：
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发表时间：
1988
期刊：
影响因子：
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作者：
J. Frehse
通讯作者：
J. Frehse