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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 2(146), Pages 3–42 (Mi umn5472)  

This article is cited in 17 scientific papers (total in 18 papers)

Boundary theory of Markov processes (the discrete case)

E. B. Dynkin


Abstract: The paper contains a detailed account of the theory of Martin boundaries for Markov processes with a countable number of states and discrete time. The probabilistic method of Hunt is used as a basis. This method is modified so as not to go outside the limits of the usual notion of a Markov process. The generalization of this notion due to Hunt is discussed in the concluding section.

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English version:
Russian Mathematical Surveys, 1969, 24:2, 1–42

Bibliographic databases:

UDC: 519.2
MSC: 60J50, 60J05, 60A10, 60G42, 60G10
Received: 03.12.1968

Citation: E. B. Dynkin, “Boundary theory of Markov processes (the discrete case)”, Uspekhi Mat. Nauk, 24:2(146) (1969), 3–42; Russian Math. Surveys, 24:2 (1969), 1–42

Citation in format AMSBIB
\Bibitem{Dyn69}
\by E.~B.~Dynkin
\paper Boundary theory of Markov processes (the discrete case)
\jour Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 2(146)
\pages 3--42
\mathnet{http://mi.mathnet.ru/umn5472}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=245096}
\zmath{https://zbmath.org/?q=an:0214.44502|0222.60048}
\transl
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 2
\pages 1--42
\crossref{https://doi.org/10.1070/RM1969v024n02ABEH001341}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. B. Dynkin, “The spase of exits of a Markov process”, Russian Math. Surveys, 24:4 (1969), 89–157  mathnet  crossref  mathscinet  zmath
    2. E. B. Dynkin, “Excessive measures and entry laws for a Markov process”, Math. USSR-Sb., 13:2 (1971), 209–246  mathnet  crossref  mathscinet  zmath
    3. E. B. Dynkin, “Supermartingaly so sluchainymi momentami rozhdeniya”, UMN, 26:6(162) (1971), 241–242  mathnet  mathscinet  zmath
    4. V. V. Konyukhovskii, “Some metric properties of Engel's representation”, Math. USSR-Sb., 18:2 (1972), 249–265  mathnet  crossref  mathscinet  zmath
    5. A. V. Uglanov, “A result on differentiable measures on a linear space”, Math. USSR-Sb., 29:2 (1976), 217–222  mathnet  crossref  mathscinet  zmath  isi
    6. R. S. Ismagilov, “The spectrum of dynamical systems and the Riesz products”, Math. USSR-Sb., 67:2 (1990), 341–366  mathnet  crossref  mathscinet  zmath  isi
    7. Atsushi Imai, “The Difference between Letters and a Martin Kernel of a Modulo 5 Markov Chain”, Advances in Applied Mathematics, 28:1 (2002), 82  crossref
    8. SUSANNE KOCH, “FURSTENBERG-TYPE FORMULAS OVER SHIFT SPACES”, Stoch. Dyn, 03:04 (2003), 499  crossref
    9. Atsushi Imai, Yasuhiro Kawasaki, Hiroshi Sato, “Martin Metrics on the Sierpiński Gasket”, Stoch. Dyn, 03:02 (2003), 267  crossref
    10. Sara Brofferio, Wolfgang Woess, “Positive Harmonic Functions for Semi-Isotropic Random Walks on Trees, Lamplighter Groups, and DL-Graphs”, Potential Anal, 24:3 (2006), 245  crossref  mathscinet  zmath  isi  elib
    11. Irina Ignatiouk-Robert, “Martin Boundary of a Killed Random Walk on a Half-Space”, J Theoret Probab, 21:1 (2008), 35  crossref  mathscinet  zmath  isi
    12. Blachere, S, “Asymptotic entropy and Green speed for random walks on countable groups”, Annals of Probability, 36:3 (2008), 1134  crossref  mathscinet  zmath  isi  elib
    13. Blachere S., Haissinsky P., Mathieu P., “Harmonic Measures Versus Quasiconformal Measures for Hyperbolic Groups”, Ann. Sci. Ec. Norm. Super., 44:4 (2011), 683–721  isi
    14. Palle E. T. Jorgensen, Erin P. J. Pearse, “A discrete Gauss-Green identity for unbounded Laplace operators, and the transience of random walks”, Isr. J. Math, 2012  crossref
    15. Ka-Sing Lau, Xiang-Yang Wang, “Denker–Sato type Markov chains on self-similar sets”, Math. Z, 2015  crossref
    16. È. B. Vinberg, S. E. Kuznetsov, “Evgenii (Eugene) Borisovich Dynkin (obituary)”, Russian Math. Surveys, 71:2 (2016), 345–371  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    17. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    18. Kong Sh.-L. Lau K.-S. Wong T.-K.L., “Random Walks and Induced Dirichlet Forms on Self-Similar Sets”, Adv. Math., 320 (2017), 1099–1134  crossref  isi
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