Hostname: page-component-cb9f654ff-nr592 Total loading time: 0 Render date: 2025-08-19T06:44:05.998Z Has data issue: false hasContentIssue false
  • English
  • Français

Advice to hedgehogs, or, constants can vary

Published online by Cambridge University Press:  01 August 2016

David Stirzaker
David Stirzaker*
Affiliation:
St John’s College, Oxford 0X1 3JP, e-mail: david.stirzaker@sjc.ox.ac.uk
Get access Rights & Permissions [Opens in a new window]

Extract

It is a trite but true remark to say that there are two fundamental random processes, one being the Poisson process and the other being Brownian motion. They are each fundamental in two ways; first, they do seem to describe much of the natural world very well, and second, the student is well-advised to study and master these two before going on to look at harder and more recondite processes. This note gives a brief glimpse of some aspects of the Poisson process, which is technically by far the more tractable of the two.

Information

Type
Research Article
Information
The Mathematical Gazette , Volume 84 , Issue 500 , July 2000 , pp. 197 - 210
Copyright
Copyright © The Mathematical Association 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1. De Moivre, Abraham, The doctrine of chances: or, A method of calculating the probability of events in play, Pearson, London (1718).Google Scholar
2. Poisson, Siméon D., Recherche sur la probabilité des jugements en matière criminelle et en matière civile, précédés des règles générales du calcul des probabilités, Bachelier, Paris (1837).Google Scholar
3. Ellis, Robert L., The mathematical and other writings of Robert Leslie Ellis, M. A., Ed. Walton, W., Deighton Bell, Cambridge (1863). [includes Ellis, R. L., On a question in tile theory of probabilities, Cam. Math. J. 4 (21) (1844), pp. 127–133.]Google Scholar
4. von Bortkiewicz, Ladislaus, Das Gesetz der kleinen Zahlen, Teubner, Leipzig (1898).Google Scholar
5. Newcomb, S., Notes on the theory of probabilities, The Mathematical Monthly, 2 (1860) pp. 134–140.Google Scholar
6. Bateman, H., Note on the probability distribution of α-particles, Phil. Mag. 20 (6) (1910) pp. 704–707, [Follows the paper by Geiger, H. and Rutherford, E., Phil. Mag. 20 (6), pp. 698-704].Google Scholar
7. Czuber, E., Die Entwicklung der Wahrscheinlichkeitstheorie und ihrer Anwendungen. Bericht, etc. B. G. Teubner, Leipzig (1899).Google Scholar
8. Czuber, E., Wahrscheinlichkeitsrechnung und ihre Anwendung auf Fehlerausgleichung, Statistik und Lebensversicherung, second edn. Two vols. Leipzig (1908–10).Google Scholar
9. Campbell, N. R., The study of discontinuous phenomena, Proc. Cam. Phil. Soc. 15, (1909) pp. 117–136.Google Scholar
10. Stigler, S. M., Stigler’s law of eponymy. Trans. N.Y. Acad. Sei. (2nd series) 39, (1980) pp. 147–157.Google Scholar
11. Erlang, Agner K., The theory of probabilities and telephone conversations, Nyt. Tidsskr. Mat. B. 20 (1909) pp. 33–41. [Reprinted in English in Brockmeyer, E., Haistrom, H.L. and Jensen, A., The Life and Works of A. K. Erlang, Copenhagen Tel. Co. (1948)]Google Scholar
12. Schottky, W., Spontaneous current fluctuations in electric conductors, [in German], Annalen der Physik, 57, (1918) pp. 541–567.Google Scholar
13. Clarke, R. D., An application of the Poisson distribution, J. Inst. Act. 72, (1946) p. 48.Google Scholar
14. Kolmogorov, A., Über die analytischen Methoden in der Wahrscheinlichskeitsrechnung, Math. Ann. 104, (1931) pp. 415–458.Google Scholar
15. Feller, W., Introduction to probability and its applications vol. I. (1st edn) Wiley, New York (1950).Google Scholar
16. Feller, William, On the integro-differential equations of purely discontinuous Markov processes. Trans. Am. Math. Soc. 48, (1940) pp. 488–515.Google Scholar
17. Tanner, J. C., The delay to pedestrians crossing a road, Biometrika 38, (1951) pp. 383–392.Google Scholar
18. Crofton, M. W., Article ‘Probability’ in Encyclopaedia Britannica, 9th edn (1885).Google Scholar
19. Haight, F. A., Handbook of the Poisson distribution, Wiley, New York (1967).Google Scholar
20. Kingman, J. F. C., Poisson processes, Clarendon Press, Oxford (1993).Google Scholar