Skip to main content
SpringerLink
Log in

On a class of measure-valued processes: singular cases

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

A measure-valued diffusion process describing how the measures evolve under flows or “imaginary” flows on R d is constructed in this paper. The interest of the process is that on the one hand, it can be viewed as a measure-valued flow; on the other hand, the general stochastic flows of measurable maps or kernels do not cover it.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dawson D A. Measure-valued Markov Processes. Lect Note Math, Vol 1541. Berlin: Springer-Verlag, 1993

    Google Scholar 

  2. Kunita H. Stochastic Flows and Stochastic Differential Equations. London: Camb Univ Press, 1990

    MATH  Google Scholar 

  3. Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes. New York: North Holland, 1988

    MATH  Google Scholar 

  4. Ma Z M, Xiang K N. Superprocesses of stochastic flows. Ann Prob, 2001, 29(1): 317–343

    Article  MATH  MathSciNet  Google Scholar 

  5. Viana M. Dynamics: Probabilistic and geometric perspertive (Plenary lecture of ICM 1998). In: Proceedings of the International Congress of Mathematicians. Berlin: Documenta Mathematica, 1998, Extra Volume I, 557–578

    Google Scholar 

  6. Arnold L. Random Dynamical Systems. Berlin: Springer-Verlag, 1998

    MATH  Google Scholar 

  7. Stroock D W, Varadhan S R S. Multidimensional Diffusion Processes. Berlin: Springer-Verlag, 1979

    MATH  Google Scholar 

  8. Le Jan Y, Raimond O. Flows, coalescence and noise. Ann Prob, 2004, 32(2): 1247–1315

    Article  MATH  Google Scholar 

  9. E W-N, Sinai Y. Recent results on mathematical and statistical hydrodymaics. Russian Math Surveys, 2000, 55(4): 635–666

    Article  MATH  MathSciNet  Google Scholar 

  10. Adler R. J. The geometry of random fields. Wiley Series in Probability and Mathematical Statistics. Chichester: John Wiley & Sons Ltd, 1981

    Google Scholar 

  11. Berg C, Christensen J P R, Ressel P. Harmonic Analysis on Semigroups. Berlin: Springer-Verlag, 1984

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    Wang Bin, Xiang Kainan & Yang Xiangqun

Authors
  1. Wang Bin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiang Kainan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Xiangqun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wang Bin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, B., Xiang, K. & Yang, X. On a class of measure-valued processes: singular cases. SCI CHINA SER A 49, 1315–1326 (2006). https://doi.org/10.1007/s11425-006-1315-y

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-006-1315-y

Keywords

Search

Navigation