平均活力定理和二阶汉密尔顿-雅可比方程

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-06-05 DOI:10.1137/23m1550438

Christian Keller

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 3 期第 1615-1642 页，2024 年 6 月。摘要。我们引入了受控随机微分方程的平均可行度概念，并建立了南云经典可行度定理的对应定理（平均可行度的必要条件和充分条件）。作为应用，我们对二阶全非线性路径依赖哈密顿-雅各比-贝尔曼方程的或然解和粘性解的比较原理和存在性进行了纯概率证明。我们没有使用紧凑性和最优停止论证，这些论证通常在关于二阶路径依赖 PDE 的粘性解的文献中使用。

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Mean Viability Theorems and Second-Order Hamilton–Jacobi Equations

SIAM Journal on Control and Optimization, Volume 62, Issue 3, Page 1615-1642, June 2024.
Abstract. We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo’s classical viability theorems (necessary and sufficient conditions for mean viability). As an application, we provide a purely probabilistic proof of a comparison principle and of existence for contingent and viscosity solutions of second-order fully nonlinear path-dependent Hamilton–Jacobi–Bellman equations. We do not use compactness and optimal stopping arguments, which are usually employed in the literature on viscosity solutions for second-order path-dependent PDEs.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.