A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.

Classification: 91A15, 49N25, 49L20

Keywords: stochastic differential game, impulse control, quasi-variational inequalities, viscosity solution

@article{COCV_2011__17_3_749_0, author = {Zhang, Feng}, title = {Stochastic differential games involving impulse controls}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {17}, number = {3}, year = {2011}, pages = {749-760}, doi = {10.1051/cocv/2010023}, zbl = {1223.93121}, mrnumber = {2826978}, language = {en}, url = {http://www.numdam.org/item/COCV_2011__17_3_749_0} }

Zhang, Feng. Stochastic differential games involving impulse controls. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, pp. 749-760. doi : 10.1051/cocv/2010023. http://www.numdam.org/item/COCV_2011__17_3_749_0/

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