September 2018, 8(3&4): 491-500. doi: 10.3934/mcrf.2018048

Jiongmin Yong's mathematical works in recent thirty years

School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang Province, China

Received  August 2018 Revised  September 2018 Published  September 2018

Citation: Shuping Chen. Jiongmin Yong's mathematical works in recent thirty years. Mathematical Control & Related Fields, 2018, 8 (3&4) : 491-500. doi: 10.3934/mcrf.2018048
References:
[1]

J.-M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Appl. Appl., 44 (1973), 384-404. doi: 10.1016/0022-247X(73)90066-8.

[2]

E. CasasL. A. Fernández and J. Yong, Optimal control of quasilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A., 125 (1995), 545-565. doi: 10.1017/S0308210500032674.

[3]

S. ChenX. LiS. Peng and J. Yong, A linear quadratic optimal control problem with disturbances—an algebraic Riccati equation and differential games approach, Appl. Math. Optim., 30 (1994), 267-305. doi: 10.1007/BF01183014.

[4]

H. O. Fattorini, Infinite Dimensional Optimization and Control Theory, Cambridge University Press, 1999. doi: 10.1017/CBO9780511574795.

[5]

A. FriedmanS. Huang and J. Yong, Optimal periodic control for the two-phase Stefan problem, SIAM J. Control Optim., 26 (1988), 23-41. doi: 10.1137/0326002.

[6]

X. FuJ. Yong and X. Zhang, Exact controllability for the multidimensional semilinear hyperbolic equations, SIAM J. Control Optim., 46 (2007), 1578-1614. doi: 10.1137/040610222.

[7]

B. Hu and J. Yong, Pontryagin maximum principle for semilinear and quasilinear parabolic equations with pointwise state constraints, SIAM J. Control Optim., 33 (1995), 1857-1880. doi: 10.1137/S0363012993250074.

[8]

S. LenhartJ. Xiong and J. Yong, Optimal control for stochastic partial differential equations with an application in controlling rabbit population, SIAM J. Control Optim., 54 (2016), 495-535. doi: 10.1137/15M1010233.

[9]

X. Li and J. Yong, Necessary conditions for optimal control of distributed parameter systems, SIAM J. Control Optim., 29 (1991), 895-908. doi: 10.1137/0329049.

[10]

X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems, Birkhäuser, Boston, 1995. doi: 10.1007/978-1-4612-4260-4.

[11]

D. Liu and J. Yong, Mathematical Finance, Shanghai People's Press, Shanghai, 2003, (in Chinese).

[12]

H. Lou and J. Yong, Optimality conditions for semilinear elliptic equations with leading term containing controls, SIAM J. Control Optim., 48 (2009), 2366-2387. doi: 10.1137/080740301.

[13]

Q. Lü, J. Yong and X. Zhang, Representation of Itô integrals by Lebesgue/Bochner integrals, J. Eur. Math. Soc., 14 (2012), 1795-1823. (Erratum: J. Eur. Math. Soc., 20 (2018), 259-260). doi: 10.4171/JEMS/765.

[14]

J. MaP. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly—a four step scheme, Probab. Theory Related Fields., 98 (1994), 339-359. doi: 10.1007/BF01192258.

[15]

J. Ma and J. Yong, Solvability of forward-backward SDEs and the nodal set of Hamilton-Jacobi-Bellman equations, Chin. Ann. Math. Ser. B., 16 (1995), 279-298.

[16]

J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Springer-Verlag, Berlin, 1999.

[17]

L. S. Pontryagin, Optimal processes of regulation, (Russian) 1960 Proc. Internat. Congress, Math., Cambridge Univ. Press, New York, 1960,182-202.

[18]

L. Pontryagin, Les jeux différentiels linéaires (French), Actes du Congrés International des Mathématiciens 1970, Tome 1. Gauthier-Villars, Paris, 1971,163-171.

[19]

S. Peng, Backward stochastic differential equation, nonlinear expectation and their applications, Proceedings of the International Congress of Mathematicians 2010, Vol. I. Hindustan Book Agency, New Delhi, 2010,393-432.

[20]

J. Yong, On Differential Games of Evasion and Pursuit, Thesis (Ph. D.)-Purdue University, 1986.

[21]

J. Yong, On differential evasion games, SIAM J. Control Optim., 26 (1988), 1-22. doi: 10.1137/0326001.

[22]

J. Yong, On differential pursuit games, SIAM J. Control Optim., 26 (1988), 478-495. doi: 10.1137/0326029.

[23]

J. Yong, Infinite-dimensional Volterra-Stieltjes evolution equations and related optimal control problems, SIAM J. Control Optim., 31 (1993), 539-568. doi: 10.1137/0331025.

[24]

J. Yong, Finding adapted solutions of forward-backward stochastic differential equations: method of continuation, Probab. Theory Related Fields., 107 (1997), 537-572. doi: 10.1007/s004400050098.

[25]

J. Yong, Linear forward-backward stochastic differential equations with random coefficients, Probab. Theory Related Fields., 135 (2006), 53-83. doi: 10.1007/s00440-005-0452-5.

[26]

J. Yong, Backward stochastic Volterra integral equations and some related problems, Stoch. Proc. Appl., 116 (2006), 779-795. doi: 10.1016/j.spa.2006.01.005.

[27]

J. Yong, Backward stochastic Volterra integral equations and some related problems, Probab. Theory Related Fields, 142 (2008), 21-77. doi: 10.1007/s00440-007-0098-6.

[28]

J. Yong, Forward backward stochastic differential equations with mixed initial and terminal conditions, Trans. Amer. Math. Soc., 362 (2010), 1047-1096. doi: 10.1090/S0002-9947-09-04896-X.

[29]

J. Yong, Optimality variational principle for optimal controls of forward-backward stochastic differential equations, SIAM J. Control Optim., 48 (2010), 4119-4156. doi: 10.1137/090763287.

[30]

J. Yong, A deterministic linear quadratic time-inconsistent optimal control problem, Math. Control Relat. Fields., 1 (2011), 83-118. doi: 10.3934/mcrf.2011.1.83.

[31]

J. Yong, Time-inconsistent optimal control problems and the equilibrium HJB equation, Math. Control Relat. Fields., 2 (2012), 271-329. doi: 10.3934/mcrf.2012.2.271.

[32]

J. Yong, Time-inconsistent optimal control problems, Proceedings of the International Congress of Mathematicians 2014, Seoul, Korea, 4 (2014), 947-969.

[33]

J. Yong, Differential Games, A Concise Introduction, World Scientific Publisher, Singapore, 2015. doi: 10.1142/9121.

[34]

J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations—time-consistent solutions, Trans. Amer. Math. Soc., 369 (2017), 5467-5523. doi: 10.1090/tran/6502.

[35]

J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999. doi: 10.1007/978-1-4612-1466-3.

show all references

References:
[1]

J.-M. Bismut, Conjugate convex functions in optimal stochastic control, J. Math. Appl. Appl., 44 (1973), 384-404. doi: 10.1016/0022-247X(73)90066-8.

[2]

E. CasasL. A. Fernández and J. Yong, Optimal control of quasilinear parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A., 125 (1995), 545-565. doi: 10.1017/S0308210500032674.

[3]

S. ChenX. LiS. Peng and J. Yong, A linear quadratic optimal control problem with disturbances—an algebraic Riccati equation and differential games approach, Appl. Math. Optim., 30 (1994), 267-305. doi: 10.1007/BF01183014.

[4]

H. O. Fattorini, Infinite Dimensional Optimization and Control Theory, Cambridge University Press, 1999. doi: 10.1017/CBO9780511574795.

[5]

A. FriedmanS. Huang and J. Yong, Optimal periodic control for the two-phase Stefan problem, SIAM J. Control Optim., 26 (1988), 23-41. doi: 10.1137/0326002.

[6]

X. FuJ. Yong and X. Zhang, Exact controllability for the multidimensional semilinear hyperbolic equations, SIAM J. Control Optim., 46 (2007), 1578-1614. doi: 10.1137/040610222.

[7]

B. Hu and J. Yong, Pontryagin maximum principle for semilinear and quasilinear parabolic equations with pointwise state constraints, SIAM J. Control Optim., 33 (1995), 1857-1880. doi: 10.1137/S0363012993250074.

[8]

S. LenhartJ. Xiong and J. Yong, Optimal control for stochastic partial differential equations with an application in controlling rabbit population, SIAM J. Control Optim., 54 (2016), 495-535. doi: 10.1137/15M1010233.

[9]

X. Li and J. Yong, Necessary conditions for optimal control of distributed parameter systems, SIAM J. Control Optim., 29 (1991), 895-908. doi: 10.1137/0329049.

[10]

X. Li and J. Yong, Optimal Control Theory for Infinite Dimensional Systems, Birkhäuser, Boston, 1995. doi: 10.1007/978-1-4612-4260-4.

[11]

D. Liu and J. Yong, Mathematical Finance, Shanghai People's Press, Shanghai, 2003, (in Chinese).

[12]

H. Lou and J. Yong, Optimality conditions for semilinear elliptic equations with leading term containing controls, SIAM J. Control Optim., 48 (2009), 2366-2387. doi: 10.1137/080740301.

[13]

Q. Lü, J. Yong and X. Zhang, Representation of Itô integrals by Lebesgue/Bochner integrals, J. Eur. Math. Soc., 14 (2012), 1795-1823. (Erratum: J. Eur. Math. Soc., 20 (2018), 259-260). doi: 10.4171/JEMS/765.

[14]

J. MaP. Protter and J. Yong, Solving forward-backward stochastic differential equations explicitly—a four step scheme, Probab. Theory Related Fields., 98 (1994), 339-359. doi: 10.1007/BF01192258.

[15]

J. Ma and J. Yong, Solvability of forward-backward SDEs and the nodal set of Hamilton-Jacobi-Bellman equations, Chin. Ann. Math. Ser. B., 16 (1995), 279-298.

[16]

J. Ma and J. Yong, Forward-Backward Stochastic Differential Equations and Their Applications, Springer-Verlag, Berlin, 1999.

[17]

L. S. Pontryagin, Optimal processes of regulation, (Russian) 1960 Proc. Internat. Congress, Math., Cambridge Univ. Press, New York, 1960,182-202.

[18]

L. Pontryagin, Les jeux différentiels linéaires (French), Actes du Congrés International des Mathématiciens 1970, Tome 1. Gauthier-Villars, Paris, 1971,163-171.

[19]

S. Peng, Backward stochastic differential equation, nonlinear expectation and their applications, Proceedings of the International Congress of Mathematicians 2010, Vol. I. Hindustan Book Agency, New Delhi, 2010,393-432.

[20]

J. Yong, On Differential Games of Evasion and Pursuit, Thesis (Ph. D.)-Purdue University, 1986.

[21]

J. Yong, On differential evasion games, SIAM J. Control Optim., 26 (1988), 1-22. doi: 10.1137/0326001.

[22]

J. Yong, On differential pursuit games, SIAM J. Control Optim., 26 (1988), 478-495. doi: 10.1137/0326029.

[23]

J. Yong, Infinite-dimensional Volterra-Stieltjes evolution equations and related optimal control problems, SIAM J. Control Optim., 31 (1993), 539-568. doi: 10.1137/0331025.

[24]

J. Yong, Finding adapted solutions of forward-backward stochastic differential equations: method of continuation, Probab. Theory Related Fields., 107 (1997), 537-572. doi: 10.1007/s004400050098.

[25]

J. Yong, Linear forward-backward stochastic differential equations with random coefficients, Probab. Theory Related Fields., 135 (2006), 53-83. doi: 10.1007/s00440-005-0452-5.

[26]

J. Yong, Backward stochastic Volterra integral equations and some related problems, Stoch. Proc. Appl., 116 (2006), 779-795. doi: 10.1016/j.spa.2006.01.005.

[27]

J. Yong, Backward stochastic Volterra integral equations and some related problems, Probab. Theory Related Fields, 142 (2008), 21-77. doi: 10.1007/s00440-007-0098-6.

[28]

J. Yong, Forward backward stochastic differential equations with mixed initial and terminal conditions, Trans. Amer. Math. Soc., 362 (2010), 1047-1096. doi: 10.1090/S0002-9947-09-04896-X.

[29]

J. Yong, Optimality variational principle for optimal controls of forward-backward stochastic differential equations, SIAM J. Control Optim., 48 (2010), 4119-4156. doi: 10.1137/090763287.

[30]

J. Yong, A deterministic linear quadratic time-inconsistent optimal control problem, Math. Control Relat. Fields., 1 (2011), 83-118. doi: 10.3934/mcrf.2011.1.83.

[31]

J. Yong, Time-inconsistent optimal control problems and the equilibrium HJB equation, Math. Control Relat. Fields., 2 (2012), 271-329. doi: 10.3934/mcrf.2012.2.271.

[32]

J. Yong, Time-inconsistent optimal control problems, Proceedings of the International Congress of Mathematicians 2014, Seoul, Korea, 4 (2014), 947-969.

[33]

J. Yong, Differential Games, A Concise Introduction, World Scientific Publisher, Singapore, 2015. doi: 10.1142/9121.

[34]

J. Yong, Linear-quadratic optimal control problems for mean-field stochastic differential equations—time-consistent solutions, Trans. Amer. Math. Soc., 369 (2017), 5467-5523. doi: 10.1090/tran/6502.

[35]

J. Yong and X. Y. Zhou, Stochastic Controls: Hamiltonian Systems and HJB Equations, Springer-Verlag, New York, 1999. doi: 10.1007/978-1-4612-1466-3.

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