The age functional for Markov chains

  • J. Theodore Cox


Markov Chain Stochastic Process Probability Theory Mathematical Biology 


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  1. 1.
    Athreya, K., Ney, P.: Branching Processes. New York: Springer 1972Google Scholar
  2. 2.
    Billingsley, P.: Convergence of Probability Measures. New York: Wiley 1968Google Scholar
  3. 3.
    Cox, J.T.: An example of phase transition in countable one dimensional Markov random fields. J. Appl. Probability 14, 205–211 (1977)Google Scholar
  4. 4.
    Cox, J.T.: Entrance laws for Markov chains. Ann. Probability 5, 533–549 (1977)Google Scholar
  5. 5.
    Cox, J.T.: An alternate proof of a theorem of Kesten concerning Markov random fields. [To appear: Ann. Probability]Google Scholar
  6. 6.
    Doob, J.B.: Stochastic Processes. New York: Wiley 1953Google Scholar
  7. 7.
    Dynkin, E.B.: Entrance and exit spaces for a Markov process. Actes. Congress Int. Math. 2, 507–512 (1970)Google Scholar
  8. 8.
    Dynkin, E.B.: The initial and final behavior of trajectories of a Markov process. Russian Math. Surveys 26, 165–182 (1971)Google Scholar
  9. 9.
    Dynkin, E.B.: Sufficient Statistics and extreme points. Ann. Probability 6, 705–730 (1978)Google Scholar
  10. 10.
    Kemperman, J.H.B.: On the age, entropies, and Supermartingales of Markov chains. Address at 1976 meeting of the New York State Probability Association, Cornell University (1976)Google Scholar
  11. 11.
    Kesten, H.: Existence and uniqueness of countable one-dimensional Markov random fields. Ann. Probability 4, 557–569 (1976)Google Scholar
  12. 12.
    Levikson, B.: The age distribution of a Markov process J. Appl. Probability 14, 492–506 (1977)Google Scholar
  13. 13.
    Liggett, T.: Random Invariant measures for Markov chains and independent particle systems. PreprintGoogle Scholar
  14. 14.
    Orey, S.: Limit Theorems for Markov Chain Transition Probabilities. New York: Van Nostrand, 1971Google Scholar
  15. 15.
    Revuz, D.: Markov Chains. Amsterdam: North Holland Publishing Company 1975Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • J. Theodore Cox
    • 1
  1. 1.Mathematics Dept.University of Southern CaliforniaLos AngelesUSA

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