Abstract
This paper considers a continuous-time stochastic hybrid system, controlled by two players with opposite objectives (zero-sum game). The parameters of the system may jump at discrete moments of time according to a Markov decision process, namely, a Markov chain that is directly controlled by both players and has finite state and action spaces. Assuming that the length of the intervals between the jumps is defined by a small parameterethe value of this game is shown to have a limit as the small parameter tends to O. This limit is established to coincide with the viscosity solution of some Hamilton—Jacobi-type equations.
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Nguyen, MT., Altman, E., Gaitsgory, V. (2001). On Stochastic Hybrid Zero-Sum Games with Nonlinear Slow Dynamics. In: Altman, E., Pourtallier, O. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 6. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0155-7_9
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DOI: https://doi.org/10.1007/978-1-4612-0155-7_9
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