奇异后向随机非线性 Volterra 积分方程的 Picard 近似算法

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-05-11 DOI:10.1007/s12346-024-01043-7

Arzu Ahmadova, Nazim I. Mahmudov

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引用次数: 0

摘要

在本文中，我们证明了具有全局 Lipschitz 连续非线性的 BSDE 的 Picard 迭代会以指数级速度收敛到解。我们在本文中的主要结果是建立了一个基本 Lemma，以证明在比希尔伯特空间中的 Lipschitz 条件更弱的条件下，阶数为 \(α \in (\frac{1}{2},1)\) 的奇异后向随机非线性 Volterra 积分方程（简称奇异 BSVIE）的适应解的全局存在性和唯一性。

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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Picard Approximation of a Singular Backward Stochastic Nonlinear Volterra Integral Equation

In this paper we prove that Picard iterations of BSDEs with globally Lipschitz continuous nonlinearities converge exponentially fast to the solution. Our main result in this paper is to establish a fundamental lemma to prove the global existence and uniqueness of an adapted solution to a singular backward stochastic nonlinear Volterra integral equation (for short, singular BSVIE) of order \(\alpha \in (\frac{1}{2},1)\) under a weaker condition than Lipschitz one in Hilbert space.

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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.