메뉴 건너뛰기




Volumn 172, Issue 2, 2000, Pages 466-510

Hamilton-Jacobi-Bellman Equations for the Optimal Control of the Duncan-Mortensen-Zakai Equation

Author keywords

Duncan Mortensen Zakai equation; Hamilton Jacobi Bellman equations; Optimal control of partially observed systems; Viscosity solutions

Indexed keywords


EID: 0000709786     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2000.3562     Document Type: Article
Times cited : (33)

References (41)
  • 1
    • 0030672454 scopus 로고    scopus 로고
    • On filtering equations for infinite dimensions
    • N. U. Ahmed, M. Fuhrman, and J. Zabczyk, On filtering equations for infinite dimensions, J. Funct. Anal. 143(1) (1997), 180-204.
    • (1997) J. Funct. Anal. , vol.143 , Issue.1 , pp. 180-204
    • Ahmed, N.U.1    Fuhrman, M.2    Zabczyk, J.3
  • 3
    • 0002984608 scopus 로고
    • On a functional analysis approach to parabolic equations in infinite dimensions
    • P. Cannarsa and G. Da Prato, On a functional analysis approach to parabolic equations in infinite dimensions, J. Funct. Anal. 118(1) (1993), 22-42.
    • (1993) J. Funct. Anal. , vol.118 , Issue.1 , pp. 22-42
    • Cannarsa, P.1    Da Prato, G.2
  • 4
    • 0026118706 scopus 로고
    • Second order Hamilton-Jacobi equations in infinite dimensions
    • P. Cannarsa and G. Da Prato, Second order Hamilton-Jacobi equations in infinite dimensions, SIAM J. Control Optim. 29(2) (1991), 474-492.
    • (1991) SIAM J. Control Optim. , vol.29 , Issue.2 , pp. 474-492
    • Cannarsa, P.1    Da Prato, G.2
  • 5
    • 0030291175 scopus 로고    scopus 로고
    • Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems in parabolic type
    • P. Cannarsa and M. E. Tessitore, Infinite dimensional Hamilton-Jacobi equations and Dirichlet boundary control problems in parabolic type, SIAM J. Control Optim. 34 (1996), 1831-1847.
    • (1996) SIAM J. Control Optim. , vol.34 , pp. 1831-1847
    • Cannarsa, P.1    Tessitore, M.E.2
  • 6
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. G. Crandall, H. Ishii, and P. L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. 27(1) (1992), 1-67.
    • (1992) Bull. Amer. Math. Soc. , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 7
    • 0001871164 scopus 로고
    • On partial sup-convolutions, a lemma of P. L. Lions and viscosity solutions in Hilbert spaces
    • M. G. Grandall, M. Kocan, and A. Świȩch, On partial sup-convolutions, a lemma of P. L. Lions and viscosity solutions in Hilbert spaces, Adv. Math. Sci. Appl. 3 (1993/4), 1-15.
    • (1993) Adv. Math. Sci. Appl. , vol.3 , pp. 1-15
    • Grandall, M.G.1    Kocan, M.2    Świȩch, A.3
  • 8
    • 44949288472 scopus 로고
    • Hamilton-Jacobi equations in infinite dimensions. Part IV: Hamiltonians with unbounded linear terms
    • M. G. Grandall and P. L. Lions, Hamilton-Jacobi equations in infinite dimensions. Part IV: Hamiltonians with unbounded linear terms, J. Funct. Anal. 90 (1990), 237-283. Part V: Unbounded linear terms and B-continuous solutions, J. Funct. Anal. 97(2) (1991), 417-465. Part VII: The HJB equation is not always satisfied, J. Funct. Anal. 125 (1994), 111-148.
    • (1990) J. Funct. Anal. , vol.90 , pp. 237-283
    • Grandall, M.G.1    Lions, P.L.2
  • 9
    • 0001295449 scopus 로고
    • Part V: Unbounded linear terms and B-continuous solutions
    • M. G. Grandall and P. L. Lions, Hamilton-Jacobi equations in infinite dimensions. Part IV: Hamiltonians with unbounded linear terms, J. Funct. Anal. 90 (1990), 237-283. Part V: Unbounded linear terms and B-continuous solutions, J. Funct. Anal. 97(2) (1991), 417-465. Part VII: The HJB equation is not always satisfied, J. Funct. Anal. 125 (1994), 111-148.
    • (1991) J. Funct. Anal. , vol.97 , Issue.2 , pp. 417-465
  • 10
    • 0001885872 scopus 로고
    • Part VII: The HJB equation is not always satisfied
    • M. G. Grandall and P. L. Lions, Hamilton-Jacobi equations in infinite dimensions. Part IV: Hamiltonians with unbounded linear terms, J. Funct. Anal. 90 (1990), 237-283. Part V: Unbounded linear terms and B-continuous solutions, J. Funct. Anal. 97(2) (1991), 417-465. Part VII: The HJB equation is not always satisfied, J. Funct. Anal. 125 (1994), 111-148.
    • (1994) J. Funct. Anal. , vol.125 , pp. 111-148
  • 11
    • 0003298203 scopus 로고
    • Stochastic Equations in Infinite Dimensions
    • Cambridge University Press, Cambridge, UK
    • G. Da Prato and J. Zabczyk, "Stochastic Equations in Infinite Dimensions," Encyclopedia Math. Appl., Cambridge University Press, Cambridge, UK, 1992.
    • (1992) Encyclopedia Math. Appl.
    • Da Prato, G.1    Zabczyk, J.2
  • 12
    • 0020100112 scopus 로고
    • Nonlinear semigroup for controlled partially observed diffusions
    • W. H. Fleming, Nonlinear semigroup for controlled partially observed diffusions, SIAM J. Control Optim. 20(2) (1982), 286-301.
    • (1982) SIAM J. Control Optim. , vol.20 , Issue.2 , pp. 286-301
    • Fleming, W.H.1
  • 13
    • 0020098555 scopus 로고
    • Optimal control of partially observed diffusions
    • W. H. Fleming and E. Pardoux, Optimal control of partially observed diffusions, SIAM J. Control Optim. 20(2) (1982), 261-285.
    • (1982) SIAM J. Control Optim. , vol.20 , Issue.2 , pp. 261-285
    • Fleming, W.H.1    Pardoux, E.2
  • 15
    • 0001232993 scopus 로고
    • Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem
    • F. Gozzi, Regularity of solutions of a second order Hamilton-Jacobi equation and application to a control problem, Comm. Partial Differential Equations 20(5&6) (1995), 775-826.
    • (1995) Comm. Partial Differential Equations , vol.20 , Issue.5-6 , pp. 775-826
    • Gozzi, F.1
  • 16
    • 0033894023 scopus 로고    scopus 로고
    • Hamilton-Jacobi equations in Hilbert spaces and stochastic boundary control
    • F. Gozzi, E. Rouy, and A. Świȩch, Hamilton-Jacobi equations in Hilbert spaces and stochastic boundary control, SIAM J. Control Optim. 38(2) (2000), 400-430.
    • (2000) SIAM J. Control Optim. , vol.38 , Issue.2 , pp. 400-430
    • Gozzi, F.1    Rouy, E.2    Świȩch, A.3
  • 17
    • 0000710250 scopus 로고
    • Partially observed control of Markov processes I
    • O. Hijab, Partially observed control of Markov processes I, Stochastics 28 (1989), 123-144.
    • (1989) Stochastics , vol.28 , pp. 123-144
    • Hijab, O.1
  • 18
    • 0000710250 scopus 로고
    • Partially observed control of Markov processes II
    • O. Hijab, Partially observed control of Markov processes II, Stochastics 28 (1989), 247-262.
    • (1989) Stochastics , vol.28 , pp. 247-262
    • Hijab, O.1
  • 19
    • 0347235647 scopus 로고
    • Partially observed control of Markov processes III
    • O. Hijab, Partially observed control of Markov processes III, Ann. Probab. 18(3) (1990), 1099-1125.
    • (1990) Ann. Probab. , vol.18 , Issue.3 , pp. 1099-1125
    • Hijab, O.1
  • 20
    • 38249013039 scopus 로고
    • Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces
    • H. Ishii, Viscosity solutions for a class of Hamilton-Jacobi equations in Hilbert spaces, J. Funct. Anal. 105 (1992), 301-341.
    • (1992) J. Funct. Anal. , vol.105 , pp. 301-341
    • Ishii, H.1
  • 21
    • 84963144955 scopus 로고
    • Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces
    • H. Ishii, Viscosity solutions of nonlinear second-order partial differential equations in Hilbert spaces, Comm. Partial Differential Equations 18 (1993), 601-651.
    • (1993) Comm. Partial Differential Equations , vol.18 , pp. 601-651
    • Ishii, H.1
  • 24
    • 0002472798 scopus 로고
    • Stochastic partial differential equations and diffusion processes
    • N. V. Krylov and B. L. Rozovskii, Stochastic partial differential equations and diffusion processes, Uspekhi Mat. Nauk 37(6) (1982), 75-95; Russian Math. Surveys 37(6) (1982), 81-105.
    • (1982) Uspekhi Mat. Nauk , vol.37 , Issue.6 , pp. 75-95
    • Krylov, N.V.1    Rozovskii, B.L.2
  • 25
    • 0345974630 scopus 로고
    • N. V. Krylov and B. L. Rozovskii, Stochastic partial differential equations and diffusion processes, Uspekhi Mat. Nauk 37(6) (1982), 75-95; Russian Math. Surveys 37(6) (1982), 81-105.
    • (1982) Russian Math. Surveys , vol.37 , Issue.6 , pp. 81-105
  • 26
    • 0347866122 scopus 로고
    • Une inégalité pour les opérateurs elliptiques du second ordre
    • P.-L. Lions, Une inégalité pour les opérateurs elliptiques du second ordre, Ann. Mat. Pura Appl. 127 (1981), 1-11.
    • (1981) Ann. Mat. Pura Appl. , vol.127 , pp. 1-11
    • Lions, P.-L.1
  • 27
    • 34250087346 scopus 로고
    • Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution
    • P.-L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution, Acta Math. 161 (1988), 243-278. Part II: Optimal Control of Zakai's equation, Lecture Notes in Mathematics, Vol. 1390 (G. Da Prato and L. Tubaro, Eds.), Springer-Verlag, Berlin, 1989, 147-170. Part III: Uniqueness of viscosity solutions for general second order equations, J. Funct. Anal. 86 (1989) 1-18.
    • (1988) Acta Math. , vol.161 , pp. 243-278
    • Lions, P.-L.1
  • 28
    • 34250087346 scopus 로고
    • Part II: Optimal Control of Zakai's equation
    • (G. Da Prato and L. Tubaro, Eds.), Springer-Verlag, Berlin
    • P.-L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution, Acta Math. 161 (1988), 243-278. Part II: Optimal Control of Zakai's equation, Lecture Notes in Mathematics, Vol. 1390 (G. Da Prato and L. Tubaro, Eds.), Springer-Verlag, Berlin, 1989, 147-170. Part III: Uniqueness of viscosity solutions for general second order equations, J. Funct. Anal. 86 (1989) 1-18.
    • (1989) Lecture Notes in Mathematics , vol.1390 , pp. 147-170
  • 29
    • 34250087346 scopus 로고
    • Part III: Uniqueness of viscosity solutions for general second order equations
    • P.-L. Lions, Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: The case of bounded stochastic evolution, Acta Math. 161 (1988), 243-278. Part II: Optimal Control of Zakai's equation, Lecture Notes in Mathematics, Vol. 1390 (G. Da Prato and L. Tubaro, Eds.), Springer-Verlag, Berlin, 1989, 147-170. Part III: Uniqueness of viscosity solutions for general second order equations, J. Funct. Anal. 86 (1989) 1-18.
    • (1989) J. Funct. Anal. , vol.86 , pp. 1-18
  • 30
    • 0005583077 scopus 로고
    • Martingales and Stochastics Integrals I
    • Springer-Verlag, Berlin
    • P. A. Meyer, Martingales and Stochastics Integrals I, in "Lecture Notes in Mathematics," Vol. 284, Springer-Verlag, Berlin, 1972.
    • (1972) Lecture Notes in Mathematics , vol.284
    • Meyer, P.A.1
  • 31
    • 0025256773 scopus 로고
    • Optimal control of stochastic partial differential equations
    • N. Nagase and M. Nisio, Optimal control of stochastic partial differential equations, SIAM J. Control and Optim. 28 (1990), 186-213.
    • (1990) SIAM J. Control and Optim. , vol.28 , pp. 186-213
    • Nagase, N.1    Nisio, M.2
  • 32
    • 0343936577 scopus 로고
    • Equations of non-linear filtering and application to stochastic control with partial observation
    • Nonlinear Filtering and Stochastic Control (Cortona 1981) Springer, Berlin-New York
    • E. Pardoux, Equations of non-linear filtering and application to stochastic control with partial observation, in "Nonlinear Filtering and Stochastic Control (Cortona 1981)," pp. 208-248, Lecture Notes in Mathematics, Vol. 972, Springer, Berlin-New York, 1982.
    • (1982) Lecture Notes in Mathematics , vol.972 , pp. 208-248
    • Pardoux1
  • 33
    • 0018768309 scopus 로고
    • Stochastic partial differential equations and filtering of diffusion processes
    • E. Pardoux, Stochastic partial differential equations and filtering of diffusion processes, Stochastics 3 (1979), 127-167.
    • (1979) Stochastics , vol.3 , pp. 127-167
    • Pardoux, E.1
  • 34
    • 0001453735 scopus 로고
    • Optimization of functions on certain subsets of Banach spaces
    • C. Stegall, Optimization of functions on certain subsets of Banach spaces, Math. Ann. 236 (1978), 171-176.
    • (1978) Math. Ann. , vol.236 , pp. 171-176
    • Stegall, C.1
  • 36
    • 33947120576 scopus 로고
    • Unbounded second order partial differential equations in infinite dimensional Hilbert spaces
    • A. Świȩch, Unbounded second order partial differential equations in infinite dimensional Hilbert spaces, Comm. Partial Differential Equations 19 (1994), 1999-2036.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1999-2036
    • Świȩch, A.1
  • 39
    • 0026836919 scopus 로고
    • On the existence of optimal relaxed controls of stochastic partial differential equations
    • X. Y. Zhou, On the existence of optimal relaxed controls of stochastic partial differential equations, SIAM J. Control and Optim. 30(2) (1992), 247-261.
    • (1992) SIAM J. Control and Optim. , vol.30 , Issue.2 , pp. 247-261
    • Zhou, X.Y.1
  • 40
    • 0027697778 scopus 로고
    • On the necessary conditions of optimal controls for stochastic partial differential equations
    • X. Y. Zhou, On the necessary conditions of optimal controls for stochastic partial differential equations, SIAM J. Control and Optim. 31 (1993), 1462-1478.
    • (1993) SIAM J. Control and Optim. , vol.31 , pp. 1462-1478
    • Zhou, X.Y.1
  • 41
    • 38249013008 scopus 로고
    • A duality analysis on stochastic partial differential equations
    • X. Y. Zhou, A duality analysis on stochastic partial differential equations, J. Funct. Anal. 103 (1992), 275-293.
    • (1992) J. Funct. Anal. , vol.103 , pp. 275-293
    • Zhou, X.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.