Hostname: page-component-594f858ff7-c4bbg Total loading time: 0 Render date: 2023-06-05T10:34:53.367Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": false, "coreDisableEcommerce": false, "corePageComponentUseShareaholicInsteadOfAddThis": true, "coreDisableSocialShare": false, "useRatesEcommerce": true } hasContentIssue false
  • English

ON A GENERALIZED Q-URN MODEL

Published online by Cambridge University Press:  15 September 2014

May-Ru Chen  and
Shoou-Ren Hsiau
May-Ru Chen
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan, Republic of China E-mail: mayru@faculty.nsysu.edu.tw
Shoou-Ren Hsiau
Affiliation:
Department of Mathematics, National Changhua University of Education, No. 1, Jin-De Road, Changhua 500, Taiwan, Republic of China E-mail: srhsiau@cc.ncue.edu.tw
Get access Rights & Permissions[Opens in a new window]

Abstract

Recently, Chen, Hsiau & Yang [1] proposed a new two-urn model with red and white balls and showed that the fractions of red balls in both urns converge almost surely to the same limit. We extend the results for the two-urn model to the q-urn model (q≥3) with similar dynamics of drawing and adding balls. We use matrix forms and martingale theory to show that the fractions of red balls in all urns converge almost surely to the same limit.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 1 , January 2015 , pp. 99 - 115
Copyright
Copyright © Cambridge University Press 2014 

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.)

References

1.Chen, M.-R.Hsiau, S.-R. & Yang, T.-H. (2014). A new two-urn model. Journal of Applied Probability, 51: 590–597.CrossRefGoogle ScholarPubMed
2.Chen, M.-R. & Wei, C.-Z. (2005). A new urn model. Journal of Applied Probability, 42: 964–976.CrossRefGoogle Scholar
3.Eggenberger, F. & Pólya, G. (1923). Über die statistik verketetter vorgänge. Zeitschrift für Angewandte Mathematik und Mechanik., 1: 279–289.CrossRefGoogle Scholar
4.Kac, M. (1947). Random walk and the theory of Brownian motion, American Mathematical Monthly, 54: 369–391.CrossRefGoogle Scholar
5.Kotz, S. & Balakrishnan, N. (1997). Advances in urn models during the past two decades. In Advances in Combinatorial Methods and Applications to Probability and Statistics. Birkhäuser Boston, Cambridge, MA, U.S.A., pp. 203–257.CrossRefGoogle Scholar
6.Mahmoud, H.M. (2009). Pólya Urn Models, Boca Raton, FL: CRC Press.Google Scholar
7.Takács, L. (1979). On an urn problem of Pal and Tatiana Ehrenfest, Mathematical Proceedings of the Cambridge Philosophical Society, 86: 127–130.CrossRefGoogle Scholar