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Differential games with random time horizon
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Differential games with random time horizon : ウィキペディア英語版
Differential games with random time horizon

The games with random time horizon are a particular case of differential games.〔Petrosjan, L.A. and Murzov, N.V. (1966). ''Game-theoretic problems of mechanics''. Litovsk. Mat. Sb. 6, pp. 423–433 (in Russian).〕 In such games, the terminal time is a random variable with a given probability distribution function. Therefore, the players maximize the mathematical expectancy of the cost function. It was shown that the modified optimization problem can be reformulated as a discounted differential game over an infinite time interval〔Petrosjan L.A. and Shevkoplyas E.V. Cooperative games with random duration, Vestnik of St.Petersburg Univ., ser.1, Vol.4, 2000 (in Russian)〕〔Marín-Solano, Jesús and Shevkoplyas, Ekaterina V. ''Non-constant discounting and differential games with random time horizon''. Automatica, Vol. 47(12), December 2011, pp. 2626–2638.〕
==Notes==


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