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

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

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
2. E. B. Dynkin, “Excessive measures and entry laws for a Markov process”, Math. USSR-Sb., 13:2 (1971), 209–246
3. E. B. Dynkin, “Supermartingaly so sluchainymi momentami rozhdeniya”, UMN, 26:6(162) (1971), 241–242
4. V. V. Konyukhovskii, “Some metric properties of Engel's representation”, Math. USSR-Sb., 18:2 (1972), 249–265
5. A. V. Uglanov, “A result on differentiable measures on a linear space”, Math. USSR-Sb., 29:2 (1976), 217–222
6. R. S. Ismagilov, “The spectrum of dynamical systems and the Riesz products”, Math. USSR-Sb., 67:2 (1990), 341–366
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
8. SUSANNE KOCH, “FURSTENBERG-TYPE FORMULAS OVER SHIFT SPACES”, Stoch. Dyn, 03:04 (2003), 499
9. Atsushi Imai, Yasuhiro Kawasaki, Hiroshi Sato, “Martin Metrics on the Sierpiński Gasket”, Stoch. Dyn, 03:02 (2003), 267
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
11. Irina Ignatiouk-Robert, “Martin Boundary of a Killed Random Walk on a Half-Space”, J Theoret Probab, 21:1 (2008), 35
12. Blachere, S, “Asymptotic entropy and Green speed for random walks on countable groups”, Annals of Probability, 36:3 (2008), 1134
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
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
15. Ka-Sing Lau, Xiang-Yang Wang, “Denker–Sato type Markov chains on self-similar sets”, Math. Z, 2015
16. È. B. Vinberg, S. E. Kuznetsov, “Evgenii (Eugene) Borisovich Dynkin (obituary)”, Russian Math. Surveys, 71:2 (2016), 345–371
17. A. M. Vershik, “The theory of filtrations of subalgebras, standardness, and independence”, Russian Math. Surveys, 72:2 (2017), 257–333
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
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