马尔可夫转换系统：后向和前向-后向随机微分方程、均场相互作用和非零和微分博弈

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-01-17 DOI:10.1007/s00245-023-10101-6

Esteban J. Rolón Gutiérrez, Son Luu Nguyen, George Yin

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引用次数: 0

摘要

这项研究致力于马尔可夫开关系统。特别是后向随机微分方程（BSDE）、前向后向随机微分方程（FBSDE）、具有均场相互作用的此类方程以及相关的非零和随机均场博弈。首先，研究了具有马尔可夫切换的 BSDE、具有马尔可夫切换的 FBSDE 以及具有均值场相互作用和制度切换的 FBSDE。在单调性条件下，无需假设前向方程的非退化条件，就能获得基础方程的唯一可解性。然后，研究了具有随机系数的非零和线性-二次随机微分博弈的开环纳什均衡点的存在性。

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Markovian-Switching Systems: Backward and Forward-Backward Stochastic Differential Equations, Mean-Field Interactions, and Nonzero-Sum Differential Games

This work is devoted to Markovian-switching systems. In particular, backward stochastic differential equations (BSDEs), forward-backward stochastic differential equations (FBSDEs), such equations with mean-field interactions, and related nonzero-sum stochastic mean-field games. First, BSDEs with Markovian switching, FBSDEs with Markovian-switching, and FBSDEs with both mean-field interactions and regime-switching are examined. Unique solvability of the underlying equations is obtained under monotonicity conditions without assuming non-degeneracy condition for the forward equation. Then the existence of open-loop Nash equilibrium points for nonzero-sum linear-quadratic stochastic differential games with random coefficients is investigated.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

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.