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Bulletin of the American Mathematical Society

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Markov processes and Martin boundaries


Authors: Hiroshi Kunita and Takesi Watanabe
Journal: Bull. Amer. Math. Soc. 69 (1963), 386-391
DOI: https://doi.org/10.1090/S0002-9904-1963-10937-4
MathSciNet review: 0148113
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  • 1. R. M. Blumenthal, R. K. Getoor and H. P. McKean, Jr., Markov processes with identical hitting distributions, Illinois J. Math. 6 (1962), 402-420. MR 142157
  • 2. M. Brelot, Le problème de Dirichlet. Axiomatique et frontière de Martin, J. Math. Pures Appl. 35 (1956), 297-335. MR 100173
  • 3. J. L. Doob, Discrete potential theory and boundaries, J. Math. Mech. 8 (1959), 433-458. MR 107098
  • 4. G. A. Hunt, Markoff processes and potentials. I, III, Illinois J. Math. 1 (1957), 44-93, 2 (1958), 151-213.
  • 5. G. A. Hunt, Markoff chains and Martin boundaries, Illinois J. Math. 4 (1960), 313-340. MR 123364
  • 6. R. S. Martin, Minimal positive harmonic functions, Trans. Amer. Math. Soc. 49 (1941), 137-172. MR 3919
  • 7. P. A. Meyer, Fonctionnelles multiplicatives et additive de Markov, Ann. Inst. Fourier (Grenoble) 12 (1962), 125-230. MR 140148
  • 8. D. Ray, Resolvents, transition functions and strongly Markovian processes, Ann. of Math. (2) 70 (1959), 43-78. MR 107302
  • 9. T. Watanabe, On the theory of Martin boundaries induced by countable Markov processes, Mem. Coll. Sci. Univ. Kyoto Ser. A 33 (1960), 39-108. MR 120682
  • 10. T. Watanabe, On the equivalence of excessive functions and superharmonic functions in the theory of Markov processes. I, Proc. Japan Acad. 38 (1962), 397-401. MR 150831


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1963-10937-4

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