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A surprising poisson process arising from a species competition model

Publication ,  Journal Article
Durrett, R; Limic, V
Published in: Stochastic Processes and their Applications
December 1, 2002

Motivated by the work of Tilman (Ecology 75 (1994) 2) and May and Nowak (J. Theoret. Biol. 170 (1994) 95) we consider a process in which points are inserted randomly into the unit interval and a new point kills each point to its left independently and with probability a. Intuitively this dynamic will create a negative dependence between the number of points in adjacent intervals. However, we show that the ensemble of points converges to a Poisson process with intensity 1/(a(1 - x)), and the number of points at time t grows like (log t)/a. © 2002 Elsevier Science B.V. All rights reserved.

Duke Scholars

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

December 1, 2002

Volume

102

Issue

2

Start / End Page

301 / 309

Related Subject Headings

  • Statistics & Probability
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Durrett, R., & Limic, V. (2002). A surprising poisson process arising from a species competition model. Stochastic Processes and Their Applications, 102(2), 301–309. https://doi.org/10.1016/S0304-4149(02)00209-0
Durrett, R., and V. Limic. “A surprising poisson process arising from a species competition model.” Stochastic Processes and Their Applications 102, no. 2 (December 1, 2002): 301–9. https://doi.org/10.1016/S0304-4149(02)00209-0.
Durrett R, Limic V. A surprising poisson process arising from a species competition model. Stochastic Processes and their Applications. 2002 Dec 1;102(2):301–9.
Durrett, R., and V. Limic. “A surprising poisson process arising from a species competition model.” Stochastic Processes and Their Applications, vol. 102, no. 2, Dec. 2002, pp. 301–09. Scopus, doi:10.1016/S0304-4149(02)00209-0.
Durrett R, Limic V. A surprising poisson process arising from a species competition model. Stochastic Processes and their Applications. 2002 Dec 1;102(2):301–309.
Journal cover image

Published In

Stochastic Processes and their Applications

DOI

ISSN

0304-4149

Publication Date

December 1, 2002

Volume

102

Issue

2

Start / End Page

301 / 309

Related Subject Headings

  • Statistics & Probability
  • 1502 Banking, Finance and Investment
  • 0104 Statistics
  • 0102 Applied Mathematics