Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-07T09:55:36.001Z Has data issue: false hasContentIssue false
  • English
  • Français

Multidimensional right-shift processes

Published online by Cambridge University Press:  01 July 2016

Norman C. Severo
Norman C. Severo*
Affiliation:
State University of New York at Buffalo
Get access Rights & Permissions [Opens in a new window]

Extract

Let v be a positive integer and for each k = 1, · · ·, v let mk and Nk be a positive and a non-negative integer, respectively. Denote by S'Nk,mk the set of (mk + 1) -tuples rk = (rk,mk, · · ·, rk,1, rk,0) having non-negative components summing to Nk, and by Xk(t) = (Xk,mk(t), · · ·, Xk,1(t), Xk,0(t)) an (mk + 1)-tuple random variable taking on values only from the set S′Nk,mk.

Type
II. Some Particular Epidemic and Cell Models
Information
Advances in Applied Probability , Volume 3 , Issue 2 , Autumn 1971 , pp. 200 - 201
Copyright
Copyright © Applied Probability Trust 1971 

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

Bailey, N. T. J. (1957) The Mathematical Theory of Epidemics. Charles Griffin and Co. Ltd., London.Google Scholar
Gart, J. J. (1968) The mathematical analysis of an epidemic with two kinds of susceptibles. Biometrics 24, 557–566.Google Scholar
Severo, N. C. (1969a) Right-shift processes, Proc. Nat. Acad. Sci. 64, 1162–1164.Google Scholar
Severo, N. C. (1969b) A recursion theorem on solving differential-difference equations and applications to some stochastic processes, J. Appl. Prob. 6, 673–681.CrossRefGoogle Scholar