The Hamilton-Jacobi-Bellman Equation for a Class of Differential Games with Random Duration

E. V. Shevkoplyas

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The Hamilton-Jacobi-Bellman Equation for a Class of Differential Games with Random Duration

机译：一类具有随机持续时间的微分对策的Hamilton-Jacobi-Bellman方程

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We consider the class of differential games with random duration. We show that a problem with random game duration can be reduced to a standard problem with an infinite time horizon. A Hamilton-Jacobi-Bellman-type equation is derived for finding optimal solutions in differential games with random duration. Results are illustrated by an example of a game-theoretic model of nonrenewable resource extraction. The problem is analyzed under the assumption of Weibull-distributed random terminal time of the game.

机译：我们考虑具有随机持续时间的差分游戏的类别。我们表明，具有随机游戏持续时间的问题可以减少为具有无限时间范围的标准问题。导出了Hamilton-Jacobi-Bellman型方程，用于在具有持续时间的差分博弈中找到最佳解。通过不可再生资源提取的博弈论模型示例说明了结果。该问题是在威布尔分布的游戏随机终端时间假设下进行分析的。

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《Automation and Remote Control》 |2014年第5期|共12页
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E. V. Shevkoplyas;
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1. The Hamilton-Jacobi-Bellman Equation for a Class of Differential Games with Random Duration [J] . E. V. Shevkoplyas Automation and Remote Control . 2014,第5期

机译：一类具有随机持续时间的微分对策的Hamilton-Jacobi-Bellman方程
2. Dynkin game of stochastic differential equations with random coefficients and associated backward stochastic partial differential variational inequality [J] . Yang Z., Tang S. SIAM Journal on Control and Optimization . 2013,第1期

机译：具有随机系数和相关的后向随机偏微分变分不等式的随机微分方程的Dynkin博弈
3. On the Stabilizing Solution of Periodic Riccati Differential Equations Related to a Class of Stochastic Linear Quadratic Differential Game [J] . V. Dragan, S. Aberkane, I. Ivanov, IFAC PapersOnLine . 2017,第1期

机译：与一类随机线性二次微分方程有关的周期Riccati微分方程的稳定解
4. Power Series Solution of the Hamilton-Jacobi-Bellman Equation for Time-varying Differential-Algebraic Equations [C] . Sjoberg, J., Glad, . 2006

机译：时变微分代数方程的Hamilton-Jacobi-Bellman方程的幂级数解
5. Parameter estimation in several classes of non-Markovian random processes defined by stochastic differential equations. [D] . Reiner, Robert Charles, Jr. 2010

机译：随机微分方程定义的几类非马尔可夫随机过程的参数估计。
6. Using second-order generalized estimating equations to model heterogeneous intraclass correlation in cluster randomized trials [O] . Catherine M. Crespi, Weng Kee Wong, Shiraz I. Mishra -1

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7. Backward stochastic differential equations under super linear G-expectation and associated Hamilton-Jacobi-Bellman equations [O] . Xu, Yuhong 2010

机译：超线性下的倒向随机微分方程 G期望和相关的Hamilton-Jacobi-Bellman方程

The Hamilton-Jacobi-Bellman Equation for a Class of Differential Games with Random Duration

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