Uniform Tauberian theorem in differential games

Dmitry V. Khlopin

Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 1, pp. 92-120.

Résumé

The uniform Tauberian theorem for differential games with zero-sum is obtained. We investigated the asymptotic behaviour of value function of the game with Cesaro mean and Abel mean. Under the usual assumptions for dynamics system, we prove that uniform convergence of the first of them implies uniform convergence of the second of them to same limit. The dynamic programming principle was the cornerstone of proof.

Détail

Keywords: differential game with zero sum, Tauberian theorem, dynamic programming principle, Abel means, Cesaro means.

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