메뉴 건너뛰기




Volumn 50, Issue 4, 2012, Pages 1886-1902

A relative value iteration algorithm for nondegenerate controlled diffusions

Author keywords

Controlled diffusions; Ergodic control; Hamilton Jacobi Bellman equation; Monotone dynamical systems; Relative value iteration; Reverse martingales

Indexed keywords

CONTROLLED DIFFUSION; ERGODIC CONTROL; HAMILTON JACOBI BELLMAN EQUATION; MONOTONE DYNAMICAL SYSTEMS; RELATIVE VALUE; REVERSE MARTINGALES;

EID: 84866419009     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/110850529     Document Type: Article
Times cited : (11)

References (20)
  • 1
    • 0036287773 scopus 로고    scopus 로고
    • Learning algorithms for Markov decision processes with average cost
    • J. Abounadi, D. Bertsekas, and V. S. Borkar, Learning algorithms for Markov decision processes with average cost, SIAM J. Control Optim., 40 (2001), pp. 681-698.
    • (2001) SIAM J. Control Optim. , vol.40 , pp. 681-698
    • Abounadi, J.1    Bertsekas, D.2    Borkar, V.S.3
  • 2
    • 84902333764 scopus 로고    scopus 로고
    • Ergodic control of diffusion processes
    • Cambridge University Press, Cambridge, UK
    • A. Arapostathis, V. S. Borkar, and M. K. Ghosh, Ergodic Control of Diffusion Processes, Encyclopedia Math. Appl. 143, Cambridge University Press, Cambridge, UK, 2011.
    • (2011) Encyclopedia Math. Appl. , vol.143
    • Arapostathis, A.1    Borkar, V.S.2    Ghosh, M.K.3
  • 3
    • 0033137501 scopus 로고    scopus 로고
    • The value iteration method for countable state Markov decision processes
    • Y. Aviv and A. Federgruen, The value iteration method for countable state Markov decision processes, Oper. Res. Lett., 24 (1999), pp. 223-234.
    • (1999) Oper. Res. Lett. , vol.24 , pp. 223-234
    • Aviv, Y.1    Federgruen, A.2
  • 4
    • 0032022988 scopus 로고    scopus 로고
    • A new value iteration method for the average cost dynamic programming problem
    • D. P. Bertsekas, A new value iteration method for the average cost dynamic programming problem, SIAM J. Control Optim., 36 (1998), pp. 742-759.
    • (1998) SIAM J. Control Optim. , vol.36 , pp. 742-759
    • Bertsekas, D.P.1
  • 5
    • 3242720761 scopus 로고    scopus 로고
    • On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions
    • V. I. Bogachev, N. V. Krylov, and M. Röckner, On regularity of transition probabilities and invariant measures of singular diffusions under minimal conditions, Comm. Partial Differential Equations, 26 (2001), pp. 2037-2080.
    • (2001) Comm. Partial Differential Equations , Issue.26 , pp. 2037-2080
    • Bogachev, V.I.1    Krylov, N.V.2    Röckner, M.3
  • 6
    • 21344460828 scopus 로고
    • Exponential and uniform ergodicity of Markov processes
    • D. Down, S. P. Meyn, and R. L. Tweedie, Exponential and uniform ergodicity of Markov processes, Ann. Probab., 23 (1995), pp. 1671-1691.
    • (1995) Ann. Probab. , vol.23 , pp. 1671-1691
    • Down, D.1    Meyn, S.P.2    Tweedie, R.L.3
  • 7
    • 0003634432 scopus 로고
    • Controlled markov processes
    • Springer-Verlag, New York
    • E. B. Dynkin and A. A. Yushkevich, Controlled Markov Processes, Grundlehren Math. Wiss. 235, Springer-Verlag, New York, 1979.
    • (1979) Grundlehren Math. Wiss. , vol.235
    • Dynkin, E.B.1    Yushkevich, A.A.2
  • 8
    • 21244477580 scopus 로고    scopus 로고
    • Subgeometric ergodicity of strong Markov processes
    • G. Fort and G. O. Roberts, Subgeometric ergodicity of strong Markov processes, Ann. Appl. Probab., 15 (2005), pp. 1565-1589.
    • (2005) Ann. Appl. Probab. , vol.15 , pp. 1565-1589
    • Fort, G.1    Roberts, G.O.2
  • 9
    • 0040361064 scopus 로고    scopus 로고
    • Existence of strong solutions for Itô's stochastic equations via approximations
    • I. Gyöngy and N. Krylov, Existence of strong solutions for Itô's stochastic equations via approximations, Probab. Theory Related Fields, 105 (1996), pp. 143-158.
    • (1996) Probab. Theory Related Fields , vol.105 , pp. 143-158
    • Gyöngy, I.1    Krylov, N.2
  • 10
    • 0000073325 scopus 로고
    • Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations
    • R. Z. Hasminskiǐ, Ergodic properties of recurrent diffusion processes and stabilization of the solution of the Cauchy problem for parabolic equations, Theory Probab. Appl., 5 (1960), pp. 179-196.
    • (1960) Theory Probab. Appl. , vol.5 , pp. 179-196
    • Has'minskiǐ, R.Z.1
  • 11
    • 1642310071 scopus 로고    scopus 로고
    • Markov chains and invariant probabilities
    • Birkhäuser Verlag, Basel
    • O. Hernández-Lerma and J. B. Lasserre, Markov Chains and Invariant Probabilities, Progr. Math. 211, Birkhäuser Verlag, Basel, 2003.
    • (2003) Progr. Math. , vol.211
    • Hernández-Lerma, O.1    Lasserre, J.B.2
  • 12
    • 0007282196 scopus 로고
    • Controlled diffusion processes
    • Springer-Verlag, New York
    • N. V. Krylov, Controlled Diffusion Processes, Appl. Math. (N.Y.) 14, Springer-Verlag, New York, 1980.
    • (1980) Appl. Math. (N.Y.) , vol.14
    • Krylov, N.V.1
  • 13
    • 77952293458 scopus 로고    scopus 로고
    • Lectures on elliptic and parabolic equations in sobolev spaces
    • American Mathematical Society, Providence, RI
    • N. V. Krylov, Lectures on Elliptic and Parabolic Equations in Sobolev Spaces, Grad. Stud. Math. 96, American Mathematical Society, Providence, RI, 2008.
    • (2008) Grad. Stud. Math. , vol.96
    • Krylov, N.V.1
  • 14
    • 77955068019 scopus 로고
    • Linear and quasilinear equations of parabolic type
    • American Mathematical Society, Providence, RI
    • O. A. Ladyženskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monogr. 23, American Mathematical Society, Providence, RI, 1967.
    • (1967) Transl. Math. Monogr. , pp. 23
    • Ladyženskaja, O.A.1    Solonnikov, V.A.2    Ural'ceva, N.N.3
  • 17
    • 77249136387 scopus 로고    scopus 로고
    • Acceleration operators in the value iteration algorithms for Markov decision processes
    • O. Shlakhter, C.-G. Lee, D. Khmelev, and N. Jaber, Acceleration operators in the value iteration algorithms for Markov decision processes, Oper. Res., 58 (2010), pp. 193-202.
    • (2010) Oper. Res. , vol.58 , pp. 193-202
    • Shlakhter, O.1    Lee, C.-G.2    Khmelev, D.3    Jaber, N.4
  • 18
    • 0003270907 scopus 로고
    • Monotone dynamical systems
    • American Mathematical Society, Providence, RI
    • H. L. Smith, Monotone Dynamical Systems, Math. Surveys Monogr. 41, American Mathematical Society, Providence, RI, 1995.
    • (1995) Math. Surveys Monogr. , vol.41
    • Smith, H.L.1
  • 19
    • 85129541797 scopus 로고    scopus 로고
    • (Nonsymmetric) Dirichlet operators on L1: Existence, uniqueness and associated Markov processes
    • W. Stannat, (Nonsymmetric) Dirichlet operators on L1: Existence, uniqueness and associated Markov processes, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 28 (1999), pp. 99-140.
    • (1999) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.28
    • Stannat, W.1
  • 20
    • 0003122592 scopus 로고
    • Dynamic programming, Markov chains, and the method of successive approximations
    • D. J. White, Dynamic programming, Markov chains, and the method of successive approximations, J. Math. Anal. Appl., 6 (1963), pp. 373-376.
    • (1963) J. Math. Anal. Appl. , vol.6 , pp. 373-376
    • White, D.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.