Geodesic
Uniform Tauberian theorem in differential games
Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 1, pp. 92-120

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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.
Keywords: differential game with zero sum, Tauberian theorem, dynamic programming principle, Abel means, Cesaro means. 
@article{MGTA_2015_7_1_a5,
     author = {Dmitry V. Khlopin},
     title = {Uniform {Tauberian} theorem in differential games},
     journal = {Matemati\v{c}eska\^a teori\^a igr i e\"e prilo\v{z}eni\^a},
     pages = {92--120},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MGTA_2015_7_1_a5/}
}
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Dmitry V. Khlopin. Uniform Tauberian theorem in differential games. Matematičeskaâ teoriâ igr i eë priloženiâ, Tome 7 (2015) no. 1, pp. 92-120. http://geodesic.mathdoc.fr/item/MGTA_2015_7_1_a5/