Skip to main content

Advertisement

SpringerLink
Log in
Menu
Find a journal Publish with us
Search
Cart
  1. Home
  2. Probability Theory and Related Fields
  3. Article
Stochastic partial differential equations for some measure-valued diffusions
Download PDF
Download PDF
  • Published: September 1988

Stochastic partial differential equations for some measure-valued diffusions

  • N. Konno1 &
  • T. Shiga2 

Probability Theory and Related Fields volume 79, pages 201–225 (1988)Cite this article

  • 791 Accesses

  • 148 Citations

  • Metrics details

Summary

We consider two classes of measure-valued diffusion processes; measure-valued branching diffusions and Fleming-Viot diffusion models. When the basic space is R 1, and the drift operator is a fractional Laplacian of order 1<α≦2, we derive stochastic partial differential equations based on a space-time white noise for these two processes. The former is the expected one by Dawson, but the latter is a new type of stochastic partial differential equation.

Download to read the full article text

Working on a manuscript?

Avoid the common mistakes

References

  1. Dawson, D.A.: Stochastic evolution equations and related measure processes. J. Multivariate Anal. 5, 1–52 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Dawson, D.A.: The critical measure diffusion process. Z. Wahrscheinlichkeitstheor. Verw. Geb. 40, 125–145 (1977)

    Article  MATH  Google Scholar 

  3. Dawson, D.A., Hochberg, K.J.: The carrying dimension of a stochastis measure diffusion. Ann. Probab. 7, 693–703 (1979)

    MathSciNet  Google Scholar 

  4. Dawson, D.A., Hochberg, K.J.: Wandering random measures in the Fleming-Viot model. Ann. Probab. 10, 554–580 (1982)

    MathSciNet  Google Scholar 

  5. Fleischmann, K.: Critical behavior of measure-valued processes. Preprint 1986

  6. Fleming, W.H., Viot, M.: Some measure-valued Markov Processes in population genetics theory. Indiana Univ. Math. J. 28, 817–843 (1979)

    MathSciNet  Google Scholar 

  7. Ikeda, N., Watanabe, S.: Stochastic differential equations and diffusion processes. Tokyo: North-Holland/Kodansha 1981

    Google Scholar 

  8. Iscoe, I.: A weighted occupation time for a class of measure-valued branching processes. Probab. Th. Rel. Fields 71, 85–116 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Perkins, E.A.: A space-time property of a class of measure-valued branching diffusions. Trans. Am. Math. Soc. (in press)

  10. Reimers, M.A.: Hyper-finite methods for multi-dimensional stochastic processes. PhD Dissertation. University of British Columbia (1986)

  11. Roelly-Coppoletta, S.: A criterion of convergence of measure-valued processes: Application to measure branching processes. Stochastics 17, 43–65 (1986)

    MATH  MathSciNet  Google Scholar 

  12. Shiga, T.: A certain class of infinite dimensional diffusion processes arising in population genetics. J. Math. Soc. Japan 30, 17–25 (1987)

    MathSciNet  Google Scholar 

  13. Strook, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin Heidelberg New York: Springer, 1979

    Google Scholar 

  14. Walsh, J.B.: An introduction to stochastic partial differential equations. Lect. Notes Math., vol. 1180, pp. 265–439. Berlin Heidelberg New York: Springer 1986

    Google Scholar 

  15. Watanabe, A.: A limit theorem of branching processes and continuous state branching processes. J. Math. Kyoto Univ. 8, 141–167 (1968)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of General Education, Muroran Institute of Technology, Mizumotocho Muroran, 050, Hokkaido, Japan

    N. Konno

  2. Department of Applied Physics, Tokyo Institute of Technology, Oh-okayama Meguro, 152, Tokyo, Japan

    T. Shiga

Authors
  1. N. Konno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Shiga
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Konno, N., Shiga, T. Stochastic partial differential equations for some measure-valued diffusions. Probab. Th. Rel. Fields 79, 201–225 (1988). https://doi.org/10.1007/BF00320919

Download citation

  • Received: 25 January 1987

  • Revised: 14 March 1988

  • Issue Date: September 1988

  • DOI: https://doi.org/10.1007/BF00320919

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Differential Equation
  • Partial Differential Equation
  • Stochastic Process
  • White Noise
  • Probability Theory
Download PDF

Working on a manuscript?

Avoid the common mistakes

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Publish your research
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our imprints

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support

167.114.118.210

Not affiliated

Springer Nature

© 2023 Springer Nature