Electronic Communications in Probability

Poisson Thinning by Monotone Factors

Karen Ball

Full-text: Open access

Abstract

Let $X$ and $Y$ be Poisson point processes on the real numbers with rates $l_1$ and $l_2$ respectively. We show that if $l_1 > l_2$, then there exists a deterministic map $f$ such that $f(X)$ and $Y$ have the same distribution, the joint distribution of $(X, f(X))$ is translation-invariant, and which is monotone in the sense that for all intervals $I$, $f(X)(I) \leq X(I)$, almost surely.

Article information

Source
Electron. Commun. Probab., Volume 10 (2005), paper no. 7, 60-69.

Dates
Accepted: 16 April 2005
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465058072

Digital Object Identifier
doi:10.1214/ECP.v10-1134

Mathematical Reviews number (MathSciNet)
MR2133893

Zentralblatt MATH identifier
1110.60050

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Ball, Karen. Poisson Thinning by Monotone Factors. Electron. Commun. Probab. 10 (2005), paper no. 7, 60--69. doi:10.1214/ECP.v10-1134. https://projecteuclid.org/euclid.ecp/1465058072


Export citation

References

  • Ball, K. Monotone factors of i.i.d. processes, to appear in the Israel J. Math.
  • Ferrari, P.A., Landim, C., Thorisson, H. Poisson trees, succession lines and coalescing random walks, Ann. I. H. Poincaré-PR 40 (2004), 141-152.
  • Holroyd, A., Peres, Y. Trees and matchings from point processes, Elect. Comm. in Probab. 8 (2003), 17-27.
  • Keane, M., Smorodinsky, M. A class of finitary codes, Israel J. Math. 26 (1977) nos. 3-4, 352-371.
  • Keane, M., Smorodinsky, M. Bernoulli schemes of the same entropy are finitarily isomorphic, Ann.Math. 109 (1979), 397-406.
  • Reiss, R.-D. A course on point processes, Springer-Verlag, New York, 1993.
  • Strassen, V. The existence of probability measures with given marginals, Ann. Math. Statist. 36 (1965), 423-439.
  • Timár, Á. Tree and grid factors for general point processes, Elect. Comm. in Probab. 9 (2004), 53-59.