Skip to main content

Moving Point Patterns: The Poisson Case

  • Conference paper

Part of the book series: Studies in Classification, Data Analysis and Knowledge Organization ((STUDIES CLASS))

Abstract

Motivated by time-dependent spatial random patterns occuring in marine or terrestrial ecosystems we investigate the limiting behaviour over time of certain Poisson point processes with possible movements of points according to a stochastic process. In particular, the possibilities of equilibrium, extinction or explosion of the system are discussed.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • 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

  • Cox, D.R. and Isham, V. (1980), Point Processes. Chapman and Hall, London.

    Google Scholar 

  • Cressie, N. (1991), Statistics for Spatial Data. Wiley, N.Y.

    Google Scholar 

  • Daley, D.J., and Vere-Jones, D. (1988), An Introduction to the Theory of Point Processes. Springer, N.Y.

    Google Scholar 

  • Madras, N. (1989), Random walks with killing. Probab. Th. Related Fields 80, no. 4, 581–600.

    Article  Google Scholar 

  • Kallenberg, O. (1983), Random Measures. Ac. Press, N.Y.

    Google Scholar 

  • König, D., Schmidt, V. (1992), Zufällige Punktprozesse. Teubner Skripten zur Mathematischen Stochastik, Teubner, Stuttgart.

    Book  Google Scholar 

  • Mathar, R., and Pfeifer, D. (1990), Stochastik für Informatiker. Leitfäden und Monographien der Informatik. Teubner, Stuttgart.

    Book  Google Scholar 

  • Pfeifer, D., Bäumer, H.-P., and Albrecht, M. (1992), Spatial point processes and their applications to biology and ecology. To appear in: Modeling Geo-Biosphere Processes.

    Google Scholar 

  • Richter, O., and Söndgerath, D. (1990), Parameter Estimation in Ecology. VCH Verlagsgesellschaft, Weinheim.

    Google Scholar 

  • Tsiatefas, G.N. (1982), Zur Bestimmung des Wanderungsprozesses [Determination of the migration process]. Biometrical J. 24, no. 1, 87–92.

    Article  Google Scholar 

  • Volkova, E.I. (1984), Some asymptotic properties of branching processes with particle motion [in Russian]. Dokl. Akad. Nauk SSSR 279, no. 2, 290–293.

    Google Scholar 

  • Wiegleb, G. (1989), Explanation and prediction in vegetation science. Vegetatio 83, 17–34.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1993 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Pfeifer, D., Bäumer, HP., Albrecht, M. (1993). Moving Point Patterns: The Poisson Case. In: Opitz, O., Lausen, B., Klar, R. (eds) Information and Classification. Studies in Classification, Data Analysis and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50974-2_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-50974-2_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56736-3

  • Online ISBN: 978-3-642-50974-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics