Hostname: page-component-7479d7b7d-fwgfc Total loading time: 0 Render date: 2024-07-12T13:15:50.232Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Distribution of the Number of Zero Partial Sums

Published online by Cambridge University Press:  14 July 2016

Ora Engelberg Percus  and
Jerome K. Percus
Ora Engelberg Percus
Affiliation:
City College, City University of New York
Jerome K. Percus
Affiliation:
Courant Institute of Mathematical Sciences, New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

A weighted Markov chain technique is used to determine the general distribution of the number of tie positions in a two candidate ballot. This may be interpreted as the distribution of the number of returns to the origin in an asymmetric random walk, when the particle at each step moves μ units in the positive direction and γ units in the negative direction, given the total number of positive steps and the number of negative steps. Explicit results are obtained when γ = 1, whereas the case of μ and γ ≠ 1 is solved in the form of a generating function.

Type
Research Papers
Information
Journal of Applied Probability , Volume 6 , Issue 1 , April 1969 , pp. 162 - 176
Copyright
Copyright © Applied Probability Trust 

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] Takács, L. (1967) Combinatorial Methods in the Theory of Stochastic Processes. John Wiley and Sons, Inc., New York.Google Scholar
[2] Barton, D. E. and Mallows, C. L. (1965) Some aspects of random sequence. Ann. Math. Statist. 36, 236–260.CrossRefGoogle Scholar
[3] Whittaker, E. T. and Watson, G. N. (1952) A Course of Modern Analysis. Cambridge University Press, Cambridge, pp. 132–133.Google Scholar
[4] Engelberg, O. (1965) On some problems concerning a restricted random walk. J. Appl. Prob. 2, 396–404.CrossRefGoogle Scholar
[5] Titchmarsh, E. C. (1939) The Theory of Functions. Oxford University Press, Oxford, pp. 116–117.Google Scholar