Skip to main content
Log in

Martin boundaries for the direct product of Markov processes

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. S. A. Molchanov, “Some questions of the theory of Martin boundaries related to Markov processes,” Dissertation, Moscow State University (1966).

  2. S. A. Molchanov, “Martin boundary for a direct product of Markov chains,” Teoriya Veroyatn. i Primen.,12, No. 2, 353–358 (1967).

    Google Scholar 

  3. S. A. Molchanov, “On the Martin boundary of a direct product of Markov processes,” Uspekhi Matem. Nauk,22, No. 2, 124–125 (1967).

    Google Scholar 

  4. E. B. Dynkin, Markov Processes [in Russian], Fizmatgiz, Moscow (1963).

    Google Scholar 

  5. J. L. Doob, “Discrete potential theory and boundaries,” J. Math. and Mech.,8, 433–458 (1959).

    Google Scholar 

  6. H. Kunita and T. Watanabe, “Markov processes and Martin boundaries,” Bull. Amer. Math. Soc.,69, No. 3, 386–391 (1963).

    Google Scholar 

  7. G. Choquet, “Integral representation theorem in compact convex sets,” Ann. Inst. Fourier,10, 334–344 (1960).

    Google Scholar 

  8. J. Lamperty and J. L. Snell, “Martin boundaries for certain Markov chains,” J. Math. Soc. Japan,15, No. 2, 113–128 (1963).

    Google Scholar 

  9. J. F. C. Kingman and S. Orey, “Ratio limit theorems for Markov chains,” Proc. Amer. Math. Soc.,15, No. 6, 907–910 (1964).

    Google Scholar 

  10. Kai Lai Chung, Homogeneous Markov Chains [Russian translation], Mir, Moscow (1964).

    Google Scholar 

  11. L. Nirenberg, “Remarks on strongly elliptic partial differential equations,” Comm. Pure and Appl. Math.,8, 648–674 (1955).

    Google Scholar 

  12. A. M. Il'in, A. S. Kalashnikov and O. A. Oleinik, “Linear equations of second order of parabolic type,” Uspekhi Matem. Nauk,17, No. 3, 3–146 (1962).

    Google Scholar 

  13. S. A. Molchanov, “Martin boundary for invariant diffusion processes on a solvable group,” Teoriya Veroyatn. i Primen.,12, No. 2, 358–362 (1967).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 11, No. 2, pp. 370–380, March–April, 1970.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molchanov, S.A. Martin boundaries for the direct product of Markov processes. Sib Math J 11, 280–287 (1970). https://doi.org/10.1007/BF00967302

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00967302

Keywords

Navigation