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Volumn 56, Issue 1, 1996, Pages 77-95

An iterative aggregation/disaggregation procedure for modelling the long-term behaviour of continuous-time evanescent random processes

Author keywords

Numerical algorithm; Quasistationary distribution; V cycle

Indexed keywords


EID: 0030354990     PISSN: 00949655     EISSN: None     Source Type: Journal    
DOI: 10.1080/00949659608811781     Document Type: Article
Times cited : (3)

References (39)
  • 2
    • 0041092918 scopus 로고
    • On two classes of interacting stochastic processes arising in cancer modeling
    • Bartoszynski, R. and Puri, P. S.(1983) On two classes of interacting stochastic processes arising in cancer modeling, Adv. Appl. Probab., 15, 695-712.
    • (1983) Adv. Appl. Probab. , vol.15 , pp. 695-712
    • Bartoszynski, R.1    Puri, P.S.2
  • 4
    • 0022093129 scopus 로고
    • Iterative aggregation/disaggregation techniques for nearly uncoupled reducible systems
    • Cao, W.-L. and Stewart, W. J.(1985) Iterative aggregation/disaggregation techniques for nearly uncoupled reducible systems, J. Assoc. Comp. Mach., 32, 702-719.
    • (1985) J. Assoc. Comp. Mach. , vol.32 , pp. 702-719
    • Cao, W.-L.1    Stewart, W.J.2
  • 5
    • 0021449143 scopus 로고
    • Aggregation/disaggregation for eigenvalue problems
    • Chatelin, F. and Miranker, W. L.(1984) Aggregation/disaggregation for eigenvalue problems, SIAM J. Numer. Anal., 21, 567-582.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 567-582
    • Chatelin, F.1    Miranker, W.L.2
  • 6
    • 38249041608 scopus 로고
    • Block iterative algorithms for stochastic matrices
    • Courtois, P. J. and Semal, P.(1986) Block iterative algorithms for stochastic matrices, Lin. Alg. Appl., 76, 59-70.
    • (1986) Lin. Alg. Appl. , vol.76 , pp. 59-70
    • Courtois, P.J.1    Semal, P.2
  • 7
    • 0041092917 scopus 로고    scopus 로고
    • Note on the stochastic theory of a self-catalytic chemical reaction
    • Dambrine, S. and Moreau, M.(1981) Note on the stochastic theory of a self-catalytic chemical reaction I, Physica, 106A, 559-573; II, Physica, 106A, 574-588.
    • (1981) I, Physica , vol.106 A , pp. 559-573
    • Dambrine, S.1    Moreau, M.2
  • 8
    • 0041092917 scopus 로고    scopus 로고
    • Dambrine, S. and Moreau, M.(1981) Note on the stochastic theory of a self-catalytic chemical reaction I, Physica, 106A, 559-573; II, Physica, 106A, 574-588.
    • II, Physica , vol.106 A , pp. 574-588
  • 9
    • 0003063241 scopus 로고
    • On quasi-stationary distributions in absorbing discrete-time finite Markov chains
    • Darroch, J. N. and Seneta, E.(1965) On quasi-stationary distributions in absorbing discrete-time finite Markov chains, J. Appl. Probab., 2, 88-100.
    • (1965) J. Appl. Probab. , vol.2 , pp. 88-100
    • Darroch, J.N.1    Seneta, E.2
  • 10
    • 0001383449 scopus 로고
    • On quasi-stationary distributions in absorbing continous-time finite Markov chains
    • Darroch, J. N. and Seneta, E.(1967) On quasi-stationary distributions in absorbing continous-time finite Markov chains, J. Appl. Probab., 4, 192-196.
    • (1967) J. Appl. Probab. , vol.4 , pp. 192-196
    • Darroch, J.N.1    Seneta, E.2
  • 11
    • 0000381122 scopus 로고
    • Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes
    • van Doorn, E. A. (1991) Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes, Adv. Appl. Probab., 23, 683-700.
    • (1991) Adv. Appl. Probab. , vol.23 , pp. 683-700
    • Van Doorn, E.A.1
  • 12
    • 51249188113 scopus 로고
    • Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains
    • Flaspohler, D. C. (1974) Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains, Ann. Inst. Statist. Math., 26, 351-356.
    • (1974) Ann. Inst. Statist. Math. , vol.26 , pp. 351-356
    • Flaspohler, D.C.1
  • 13
    • 0001341538 scopus 로고
    • Sparse Cholesky factorization on a local-memory multiprocessor
    • George, A., Heath, M., Liu, J. W. H. and Ng, E. (1988) Sparse Cholesky factorization on a local-memory multiprocessor., SIAM J. Sci Stat. Comp., 9, 327-340.
    • (1988) SIAM J. Sci Stat. Comp. , vol.9 , pp. 327-340
    • George, A.1    Heath, M.2    Liu, J.W.H.3    Ng, E.4
  • 14
    • 0024281170 scopus 로고
    • Instabilities and oscillations in chemical reactions in closed and open systems
    • Gray, P. (1988) Instabilities and oscillations in chemical reactions in closed and open systems, Proc. Roy. Soc. Lond. A 415, 1-34.
    • (1988) Proc. Roy. Soc. Lond. A , vol.415 , pp. 1-34
    • Gray, P.1
  • 15
    • 0021310291 scopus 로고
    • Autocatalytic reactions in the CST R: Oscillations and instabilities in the system A + 2B → 3B; B → C
    • Gray, P. and Scott, S. K. (1984) Autocatalytic reactions in the CST R: oscillations and instabilities in the system A + 2B → 3B; B → C, Chem. Eng. Sci., 39, 1087-1097.
    • (1984) Chem. Eng. Sci. , vol.39 , pp. 1087-1097
    • Gray, P.1    Scott, S.K.2
  • 16
    • 0023399469 scopus 로고
    • Aggregation/disaggregation methods for computing the stationary distribution of a Markov chain
    • Haviv, M. (1987) Aggregation/disaggregation methods for computing the stationary distribution of a Markov chain, SIAM J. Numer. Anal., 24, 952-966.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 952-966
    • Haviv, M.1
  • 17
    • 0009560759 scopus 로고
    • Aggregation/disaggregation algorithm for computing the stationary distribution of a large Markov chain
    • Haviv, M. (1992) Aggregation/disaggregation algorithm for computing the stationary distribution of a large Markov chain. Commun. Stat. -Stochastic Models, 8, 565-575.
    • (1992) Commun. Stat. -Stochastic Models , vol.8 , pp. 565-575
    • Haviv, M.1
  • 18
    • 0002054228 scopus 로고
    • Resilience and stability of ecological systems
    • Holling, C. S. (1973) Resilience and stability of ecological systems, Ann. Rev. Ecol. Systematics, 4, 1-23.
    • (1973) Ann. Rev. Ecol. Systematics , vol.4 , pp. 1-23
    • Holling, C.S.1
  • 19
    • 0000556573 scopus 로고
    • Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains
    • Koury, J. R., McAllister, D F. and Stewart, W. J. (1984) Iterative methods for computing stationary distributions of nearly completely decomposable Markov chains, SIAM J. Discr. Alg. Methods, 5, 164-186.
    • (1984) SIAM J. Discr. Alg. Methods , vol.5 , pp. 164-186
    • Koury, J.R.1    McAllister, D.F.2    Stewart, W.J.3
  • 20
    • 0004252812 scopus 로고
    • Multigrid methods
    • Philadelphia, PA
    • McCormick, S. F. (1987) Multigrid Methods, SIAM, Philadelphia, PA.
    • (1987) SIAM
    • McCormick, S.F.1
  • 21
    • 0024680811 scopus 로고
    • Stochastic complementation, uncoupling Markov chains and the theory of nearly reducible systems
    • Meyer, C. D. (1991) Stochastic complementation, uncoupling Markov chains and the theory of nearly reducible systems, SIAM Rev., 31, 187-207.
    • (1991) SIAM Rev. , vol.31 , pp. 187-207
    • Meyer, C.D.1
  • 23
    • 0026360184 scopus 로고
    • On the stationary distributior of the Ross malaria model
    • Nå;sell, I. (1991) On the stationary distributior of the Ross malaria model, Math. Biosciences, 107, 187-207.
    • (1991) Math. Biosciences , vol.107 , pp. 187-207
    • 1    sell, I.2
  • 24
    • 0023073053 scopus 로고
    • Limit theorem for the population size of a birth and death process allowing catastrophes
    • Pakes, A. G. (1987) Limit theorem for the population size of a birth and death process allowing catastrophes, J. Math. Biol., 25, 307-325.
    • (1987) J. Math. Biol. , vol.25 , pp. 307-325
    • Pakes, A.G.1
  • 25
    • 0002706326 scopus 로고
    • Quasistationary distributions for some autocatalytic reactions
    • Parsons, R. W. and Pollett, P. K. (1987) Quasistationary distributions for some autocatalytic reactions, J. Statist. Phys., 46, 249-254.
    • (1987) J. Statist. Phys. , vol.46 , pp. 249-254
    • Parsons, R.W.1    Pollett, P.K.2
  • 26
    • 0039313517 scopus 로고
    • On the problem of evaluating quasistationary distributions for open reaction schemes
    • Pollett, P. K. (1988) On the problem of evaluating quasistationary distributions for open reaction schemes, J. Statist. Phys., 53, 1207-1215.
    • (1988) J. Statist. Phys. , vol.53 , pp. 1207-1215
    • Pollett, P.K.1
  • 27
    • 0041092796 scopus 로고
    • A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold
    • Pollett, P. K. and Roberts, A. J. (1990) A description of the long-term behaviour of absorbing continuous-time Markov chains using a centre manifold, Adv. Appl. Probab., 22, 111-128.
    • (1990) Adv. Appl. Probab. , vol.22 , pp. 111-128
    • Pollett, P.K.1    Roberts, A.J.2
  • 28
    • 0001855196 scopus 로고
    • An efficient procedure for computing quasistationary distributions of Markov chains with sparse transition structure
    • Pollett, P. K. and Stewart, D. E. (1994) An efficient procedure for computing quasistationary distributions of Markov chains with sparse transition structure, Adv. Appl. Probab., 26, 68-79.
    • (1994) Adv. Appl. Probab. , vol.26 , pp. 68-79
    • Pollett, P.K.1    Stewart, D.E.2
  • 30
    • 0002823230 scopus 로고
    • On a stochastic model of an epidemic
    • Ridler-Rowe, C. J. (1967) On a stochastic model of an epidemic, J. Appl. Probab., 4, 19-33.
    • (1967) J. Appl. Probab. , vol.4 , pp. 19-33
    • Ridler-Rowe, C.J.1
  • 34
    • 0000564723 scopus 로고
    • On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states
    • Seneta, E. and Vere-Jones, D. (1966) On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states, J. Appl. Probab., 3, 403-434.
    • (1966) J. Appl. Probab. , vol.3 , pp. 403-434
    • Seneta, E.1    Vere-Jones, D.2
  • 35
  • 36
    • 0001915826 scopus 로고
    • On a direct method for the solution of nearly uncoupled Markov chains
    • Stewart, G. W. and Zhang, G. (1991) On a direct method for the solution of nearly uncoupled Markov chains, Numer. Math., 59, 1-11.
    • (1991) Numer. Math. , vol.59 , pp. 1-11
    • Stewart, G.W.1    Zhang, G.2
  • 37
    • 0004098998 scopus 로고
    • A lumping method for numerical calculation of stationary distributions of Markov chains
    • Takahashi, Y. (1975) A lumping method for numerical calculation of stationary distributions of Markov chains, Res. Rep.. Dept. of Info. Sci., Tokyo Inst. Tech., B-18.
    • (1975) Res. Rep.. Dept. of Info. Sci., Tokyo Inst. Tech. , vol.B-18
    • Takahashi, Y.1
  • 38
    • 0009624554 scopus 로고
    • The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties
    • Tweedie, R. L. (1973) The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties, J. Appl. Probab., 10, 84-99.
    • (1973) J. Appl. Probab. , vol.10 , pp. 84-99
    • Tweedie, R.L.1
  • 39
    • 84974129208 scopus 로고
    • Some limit theorems for evanescent processes
    • Vere-Jones, D. (1969) Some limit theorems for evanescent processes, Austral. J. Statist., 11, 67-78.
    • (1969) Austral. J. Statist. , vol.11 , pp. 67-78
    • Vere-Jones, D.1


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