Skip to main content

Diffusion operators in population genetics and convergence of Markov chains

Stochastic Equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 695)

Keywords

  • Markov Chain
  • Diffusion Process
  • Population Genetic
  • Diffusion Approximation
  • Diffusion Operator

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.F. Crow and M. Kimura, An introduction to population genetics theory, Harper and Row, New York, 1970.

    MATH  Google Scholar 

  2. S.N.Ethier, An error estimate for the diffusion approximation in population genetics, Ph. D. Thesis, University of Wisconsin, 1975.

    Google Scholar 

  3. S.N. Ethier, A class of degenerate diffusion processes occurring in population genetics, Comm.Pure Appl.Math. 29 (1976), 483–493.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M.I. Freidlin, On the factorization of non-negative definite matrices, Theor. Probability Appl. 13 (1968), 354–356.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. J.H. Gillespie, Natural selection for within-generation variance in offspring number, II. Discrete haploid models, Genetics 81 (1975), 403–413.

    MathSciNet  Google Scholar 

  6. S. Karlin and J. McGregor, On some stochastic models in genetics, "Stochastic models in medicine and biology" ed. by J. Gurland, Univ. of Wisconsin Press, Madison, 1964, 245–271.

    Google Scholar 

  7. S. Karlin and J. McGregor, Direct product branching processes and related Markov chains, Proc.Nat.Acad.Sci.USA 51 (1964), 598–602.

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. M. Kimura, Diffusion models in population genetics, J.Appl. Probability 1 (1964), 177–232.

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. R.A. Littler and E.D. Fackerell, Transition densities for neutral multi-allele diffusion models, Biometrics 31 (1975), 117–123.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. N. Okada, On convergence to diffusion processes of Markov chains related to population genetics, (to appear).

    Google Scholar 

  11. K. Sato, Diffusion processes and a class of Markov chains related to population genetics, Osaka J.Math. 13 (1976), 631–659.

    MathSciNet  MATH  Google Scholar 

  12. K. Sato, A class of Markov chains related to selection in population genetics, J.Math.Soc.Japan 28 (1976), 621–637.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. K.Sato, Convergence of a class of Markov chains to mutidimensional degenerate diffusion processes, Proc. Intern.Symp.Stoch.Diff.Eg. (to appear).

    Google Scholar 

  14. K.Sato, Convergence to a diffusion of a multi-allelic model in population genetics, Adv. Appl.Probability (to appear).

    Google Scholar 

  15. N. Shimakura, Equations différentielles provenant de la génétique de population, Tohoku Math.J. 29 (1977), 287–318.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. D.W. Stroock and S.R.S. Varadhan, Diffusion processes with continuous coefficients, Comm.Pure Appl.Math. 22 (1969), 345–400 and 479–530.

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1978 Springer-Verlag

About this paper

Cite this paper

Sato, Ki. (1978). Diffusion operators in population genetics and convergence of Markov chains. In: Kallianpur, G., Kölzow, D. (eds) Measure Theory Applications to Stochastic Analysis. Lecture Notes in Mathematics, vol 695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062660

Download citation

  • DOI: https://doi.org/10.1007/BFb0062660

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09098-4

  • Online ISBN: 978-3-540-35556-4

  • eBook Packages: Springer Book Archive