Abstract

We examine the extent to which random samplings from the values of a random convex set, determine the distribution of the random set itself. Several positive results, counter-examples, open problems, and research directions, are offered.

Author information

Contact details are reproduced from the original publication and may be historical.

Keywords

  • Random sets
  • m-point sampling distribution
  • stochastic geometry

Mathematics Subject Classification

60D05, 52A22, 28B20

References

  1. S. N. Chui, D. Stoyan, W. S. Kendall, J. Mecke: Stochastic Geometry and its Applications, 3rd ed., Wiley Series in Probability and Statistics, John Wiley, Chichester (2013).https://doi.org/10.1002/9781118658222Google Scholar
  2. I. Molchanov: Theory of Random Sets, 2nd ed., Springer, London (2017).https://doi.org/10.1007/978-1-4471-7349-6Google Scholar
  3. I. Molchanov, F. Molinari: Random Sets in Econometrics, Cambridge University Press, Cambridge (2018).https://doi.org/10.1017/9781316392973Google Scholar
  4. H. T. Nguyen: An Introduction to Random Sets, Chapman and Hall/CRC, London (2006).https://doi.org/10.1201/9781420010619Google Scholar
  5. R. J-B Wets: Stochastic programming, in: Handbooks in Operation Research and Management Science, Chapter VIII, Volume 1, G. L. Nemhauser et al. (eds.), Elsevier, Amsterdam (1989) 573–629.https://doi.org/10.1016/S0927-0507(89)01009-1Google Scholar

Suggested citation

Z. Artstein, A. Shapira. “Samplings from the Values of Random Convex Sets.” Journal of Convex Analysis 30 (2023), No. 2, 441–452. https://doi.org/10.68381/jca30026

Download BibTeXPublished by Heldermann Verlag.

Published by Heldermann Verlag, 2023. Rights now held by Banach Press LLC.