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Twoperson zerosum linear quadratic stochastic differential games by a Hilbert space method
1.  Department of Mathematics, Bradley University, Peoria, IL 616125, United States 
2.  Department of Mathematics, University of Central Florida, Orlando, FL 32816, United States 
[1] 
Alain Bensoussan, Shaokuan Chen, Suresh P. Sethi. Linear quadratic differential games with mixed leadership: The openloop solution. Numerical Algebra, Control & Optimization, 2013, 3 (1) : 95108. doi: 10.3934/naco.2013.3.95 
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Tyrone E. Duncan. Some linearquadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions. Discrete & Continuous Dynamical Systems  A, 2015, 35 (11) : 54355445. doi: 10.3934/dcds.2015.35.5435 
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Dean A. Carlson. Finding openloop Nash equilibrium for variational games. Conference Publications, 2005, 2005 (Special) : 153163. doi: 10.3934/proc.2005.2005.153 
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Martino Bardi. Explicit solutions of some linearquadratic mean field games. Networks & Heterogeneous Media, 2012, 7 (2) : 243261. doi: 10.3934/nhm.2012.7.243 
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Valery Y. Glizer, Oleg Kelis. Singular infinite horizon zerosum linearquadratic differential game: Saddlepoint equilibrium sequence. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 120. doi: 10.3934/naco.2017001 
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Robert S. Anderssen, Martin Kružík. Modelling of wheatflour dough mixing as an openloop hysteretic process. Discrete & Continuous Dynamical Systems  B, 2013, 18 (2) : 283293. doi: 10.3934/dcdsb.2013.18.283 
[7] 
Jianhui Huang, Xun Li, Jiongmin Yong. A linearquadratic optimal control problem for meanfield stochastic differential equations in infinite horizon. Mathematical Control & Related Fields, 2015, 5 (1) : 97139. doi: 10.3934/mcrf.2015.5.97 
[8] 
Shigeaki Koike, Hiroaki Morimoto, Shigeru Sakaguchi. A linearquadratic control problem with discretionary stopping. Discrete & Continuous Dynamical Systems  B, 2007, 8 (2) : 261277. doi: 10.3934/dcdsb.2007.8.261 
[9] 
Russell Johnson, Carmen Núñez. Remarks on linearquadratic dissipative control systems. Discrete & Continuous Dynamical Systems  B, 2015, 20 (3) : 889914. doi: 10.3934/dcdsb.2015.20.889 
[10] 
Tijana Levajković, Hermann Mena, Amjad Tuffaha. The stochastic linear quadratic optimal control problem in Hilbert spaces: A polynomial chaos approach. Evolution Equations & Control Theory, 2016, 5 (1) : 105134. doi: 10.3934/eect.2016.5.105 
[11] 
Roberta Fabbri, Russell Johnson, Sylvia Novo, Carmen Núñez. On linearquadratic dissipative control processes with timevarying coefficients. Discrete & Continuous Dynamical Systems  A, 2013, 33 (1) : 193210. doi: 10.3934/dcds.2013.33.193 
[12] 
Galina Kurina, Sahlar Meherrem. Decomposition of discrete linearquadratic optimal control problems for switching systems. Conference Publications, 2015, 2015 (special) : 764774. doi: 10.3934/proc.2015.0764 
[13] 
Georg Vossen, Stefan Volkwein. Model reduction techniques with aposteriori error analysis for linearquadratic optimal control problems. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 465485. doi: 10.3934/naco.2012.2.465 
[14] 
Walter Alt, Robert Baier, Matthias Gerdts, Frank Lempio. Error bounds for Euler approximation of linearquadratic control problems with bangbang solutions. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 547570. doi: 10.3934/naco.2012.2.547 
[15] 
Xingwu Chen, Jaume Llibre, Weinian Zhang. Averaging approach to cyclicity of hopf bifurcation in planar linearquadratic polynomial discontinuous differential systems. Discrete & Continuous Dynamical Systems  B, 2017, 22 (10) : 39533965. doi: 10.3934/dcdsb.2017203 
[16] 
Hongyan Yan, Yun Sun, Yuanguo Zhu. A linearquadratic control problem of uncertain discretetime switched systems. Journal of Industrial & Management Optimization, 2017, 13 (1) : 267282. doi: 10.3934/jimo.2016016 
[17] 
Dejian Chang, Zhen Wu. Stochastic maximum principle for nonzero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial & Management Optimization, 2015, 11 (1) : 2740. doi: 10.3934/jimo.2015.11.27 
[18] 
Henri Bonnel, Ngoc Sang Pham. Nonsmooth optimization over the (weakly or properly) Pareto set of a linearquadratic multiobjective control problem: Explicit optimality conditions. Journal of Industrial & Management Optimization, 2011, 7 (4) : 789809. doi: 10.3934/jimo.2011.7.789 
[19] 
Rui Mu, Zhen Wu. Nash equilibrium points of recursive nonzerosum stochastic differential games with unbounded coefficients and related multiple dimensional BSDEs. Mathematical Control & Related Fields, 2017, 7 (2) : 289304. doi: 10.3934/mcrf.2017010 
[20] 
Qian Liu, Xinmin Yang, Heung Wing Joseph Lee. On saddle points of a class of augmented lagrangian functions. Journal of Industrial & Management Optimization, 2007, 3 (4) : 693700. doi: 10.3934/jimo.2007.3.693 
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