A General Theory Approach to the Construction of Markov Processes

  • Bruce W. Atkinson
Part of the Progress in Probability and Statistics book series (PRPR, volume 7)


This can be considered as the third in a series of papers exploiting the commutativity of projections for Markov processes as begun in [1] and continued in [2]. We use the projections here to address the problem of finding necessary and sufficient conditions for the existence of “very regular” Markov processes, which, among other things, serve to provide further insight into the familiar regularity assumptions of Markov process theory.


Markov Process Open Interval Random Time Markov Property Prediction Process 
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  1. 1.
    B. Atkinson. Generalized strong Markov properties and applications. Z. Wahr. verw. Geb. 60 (1982), 71–78.MATHCrossRefGoogle Scholar
  2. 2.
    B. Atkinson. Germ fields and a converse to the strong Markov property. Seminar on Stochastic Processes — 1982, pp. 1–21, Birkhauser, Boston 1983.Google Scholar
  3. 3.
    K.L. Chung and J. Glover. Left continuous moderate Markov processes. Z. Wahr. verw. Geb. 49 (1979), 237–248.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    C. Dellacherie and P. Meyer. Probabilités et Potentiel. Herman, Paris, 1980.MATHGoogle Scholar
  5. 5.
    E.B. Dynkin. Markov representations of stochastic systems. Russian Math. Surveys, 30 (1975), 65–104.MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    F. Knight. Prediction processes and an autonomous germ Markov property. Annals of Prob., 7 (1979), 385–405.MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    F. Knight. Essays on the Prediction Process. IMS Lecture Note Series, Hayward, 1981.Google Scholar
  8. 8.
    P.A. Meyer and Yen Kiaan. Generation d’une famille de tribus par un processus croissant. Séminaire de Probabilités IX, Springer-Verlag, Lecture Notes 465 (1975), 466–470.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1984

Authors and Affiliations

  • Bruce W. Atkinson
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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