Results 261 to 270 of about 132,701 (326)
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2019
In this section we present the dynamic programming approach to stochastic differential games. We only present the case for zero sum games. For the extension to non-zero sum games, we refer to [MO].
Bernt Øksendal, Agnès Sulem
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In this section we present the dynamic programming approach to stochastic differential games. We only present the case for zero sum games. For the extension to non-zero sum games, we refer to [MO].
Bernt Øksendal, Agnès Sulem
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One kind of linear-quadratic zero-sum stochastic differential game with jumps
International Journal of Control, 2020This paper is concerned with one kind of two-person zero-sum linear-quadratic stochastic differential game with jumps. A closed-loop formulation for the saddle points of the game is established in a mixed-strategy-law form, for which the associated ...
Zhiyong Yu, Baokai Zhang, Feng Zhang
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An Open-Loop Stackelberg Strategy for the Linear Quadratic Mean-Field Stochastic Differential Game
IEEE Transactions on Automatic Control, 2019This paper is concerned with the open-loop linear–quadratic (LQ) Stackelberg game of the mean-field stochastic systems in finite horizon. By means of two generalized differential Riccati equations, the follower first solves a mean-field stochastic LQ ...
Yaning Lin, Xiushan Jiang, Weihai Zhang
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A Scalar Linear-Quadratic Two Player Stochastic Differential Game with a Rosenblatt Process Noise
IEEE Conference on Decision and Control, 2020A stochastic differential game with two players on an infinite time horizon, a quadratic payoff, and a scalar linear stochastic system that includes the two players’ actions and a Rosenblatt process noise is formulated and explicitly solved.
T. Duncan, B. Pasik-Duncan
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Stochastic zero-sum differential games and backward stochastic differential equations
Random Operators and Stochastic Equations, 2023Abstract In this paper, we study the stochastic zero-sum differential game in finite horizon in a general case. We first prove that the BSDE associated with a specific generator (the Hamiltonian function for the game) has a unique solution.
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Stochastic Differential Game Techniques
1981The paper deals with the theory of stochastic differential games and includes a comprehensive review of the subject under discussion. The main aspects of stochastic differential games discussed in the paper are: problem formulation, solution concepts and the difficulties encountered in trying to obtain a solution.
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Numerical Approximations for Stochastic Differential Games
SIAM Journal on Control and Optimization, 2002The Markov chain approximation method [see for example \textit{H. J. Kushner} and \textit{P. Dupuis}, ``Numerical methods for stochastic control problems in continuous time'' (2001; Zbl 0968.93005)] is a widely used method for the numerical solution for standard forms of stochastic control problems with reflected-jump diffusion models, and converges ...
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Optimal Play in a Stochastic Differential Game
SIAM Journal on Control and Optimization, 1981This paper considers play in a two-person zero-sum differential game where the dynamics are given by a differential equation with additive white noise. Feedback strategies are employed. Standard results from control theory show that the maximizing player has an optimal response to any pre-announced strategy of the minimizing player.
Elliott, R. J., Davis, M. H. A.
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2014
In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled ...
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In this chapter, we will deal with zero-sum two-player time-homogeneous stochastic differential games and viscosity solutions of the Isaacs equations arising from such games, via the dynamic programming principle.In Sect. 4.1, we are concerned with basic concepts and definitions and we introduce stochastic differential games, referring to (Controlled ...
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Stochastic multi‐player pursuit–evasion differential games
International Journal of Robust and Nonlinear Control, 2007AbstractAutonomous aerial vehicles play an important role in military applications such as in search, surveillance and reconnaissance. Multi‐player stochastic pursuit–evasion (PE) differential game is a natural model for such operations involving intelligent moving targets with uncertainties.
Li, Dongxu +2 more
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