前后向随机方程组：一种函数不动点方法

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications Pub Date : 2023-01-02 DOI:10.1080/07362994.2021.1988857

Kihun Nam, Yunxi Xu

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引用次数: 1

摘要

摘要：我们引入了前向-后向随机方程（FBSE），该方程将完全耦合的前向-向后结构纳入Cheridito和Nam（Ann.Prob.45（6A）:3795–38282017）中引入的向后随机方程（BSE）中。该系统推广了以往文献中的经典后向随机微分方程（BSDE）和前向后向随机方程（FBSDE）。我们将FBSE转化为随机变量空间上的不动点方程，然后应用一般的不动点定理来导出解的存在性和/或唯一性。因此，我们获得了具有功能驱动器的完全耦合FBSDE的新的存在性和/或唯一性结果，这些驱动器是Lipschitz或非Lipschitz。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Forward-backward stochastic equations: a functional fixed point approach

Abstract We introduce forward-backward stochastic equations (FBSEs) that incorporate fully-coupled forward-backward structure into backward stochastic equations (BSEs) introduced in Cheridito and Nam (Ann. Probab. 45(6A):3795–3828, 2017). Such a system generalizes the classical backward stochastic differential equations (BSDEs) and forward-backward stochastic differential equations (FBSDEs) in previous literature. We transform an FBSE into a fixed point equation on the space of random variables and then apply general fixed point theorems to derive the existence and/or uniqueness of a solution. As a result, we obtain novel existence and/or uniqueness results for fully-coupled FBSDEs with functional drivers, which are either Lipschitz or non-Lipschitz.

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来源期刊

Stochastic Analysis and Applications 数学-统计学与概率论

CiteScore

2.70

自引率

7.70%

发文量

审稿时长

6-12 weeks

期刊介绍： Stochastic Analysis and Applications presents the latest innovations in the field of stochastic theory and its practical applications, as well as the full range of related approaches to analyzing systems under random excitation. In addition, it is the only publication that offers the broad, detailed coverage necessary for the interfield and intrafield fertilization of new concepts and ideas, providing the scientific community with a unique and highly useful service.