Path-Dependent Hamilton–Jacobi Equations with u-Dependence and Time-Measurable Hamiltonians

IF 1.7 2区 数学 Q2 MATHEMATICS, APPLIED
Elena Bandini, Christian Keller
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引用次数: 0

Abstract

We establish existence and uniqueness of minimax solutions for a fairly general class of path-dependent Hamilton–Jacobi equations. In particular, the relevant Hamiltonians can contain the solution and they only need to be measurable with respect to time. We apply our results to optimal control problems of (delay) functional differential equations with cost functionals that have discount factors and with time-measurable data. Our main results are also crucial for our companion paper Bandini and Keller (Non-local Hamilton–Jacobi–Bellman equations for the stochastic optimal control of path-dependent piecewise deterministic processes, 2024, http://arxiv.org/abs/2408.02147), where non-local path-dependent Hamilton–Jacobi–Bellman equations associated to the stochastic optimal control of non-Markovian piecewise deterministic processes are studied.

具有u相关和时间可测哈密顿量的路径相关哈密-雅可比方程
我们建立了一类相当一般的路径相关Hamilton-Jacobi方程极大极小解的存在唯一性。特别是,相关的哈密顿量可以包含解,它们只需要相对于时间是可测量的。我们将我们的结果应用于(延迟)泛函微分方程的最优控制问题,这些方程具有折扣因子和具有时间可测量数据的成本泛函。我们的主要结果对于我们的同伴论文Bandini和Keller(路径依赖分段确定性过程随机最优控制的非局部Hamilton-Jacobi-Bellman方程,2024,http://arxiv.org/abs/2408.02147)也至关重要,其中研究了与非马尔可夫分段确定性过程随机最优控制相关的非局部路径依赖Hamilton-Jacobi-Bellman方程。
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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来源期刊
CiteScore
3.30
自引率
5.60%
发文量
103
审稿时长
>12 weeks
期刊介绍: The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.
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