Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-27T08:06:45.598Z Has data issue: false hasContentIssue false
  • English
  • Français

MONOTONICITY IN LAG FOR NONMONOTONE MARKOV CHAINS

Published online by Cambridge University Press:  01 October 2004

Rafał Kulik
Rafał Kulik
Affiliation:
Mathematical Institute, University of Wrocław, Wrocław, Poland, E-mail: [email protected], and, Department of Mathematics and Statistics, University of Ottawa, K1N 6N5 Ottawa, Ontario, Canada, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

It is well known that for a stochastically monotone Markov chain {Jn}n≥1 a function γ(n) = Cov[f (J1),g(Jn)] is decreasing if f and g are increasing. We prove this property for a special subclass of nonmonotone double stochastic Markov chains.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 18 , Issue 4 , October 2004 , pp. 485 - 492
Copyright
© 2004 Cambridge University Press

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

REFERENCES

Bergmann, R. & Stoyan, D. (1978). Monotonicity properties of second order characteristics of stochastically monotone Markov chains. Mathematische Nachrichten 82: 99–102.Google Scholar
Daley, D.J. (1968). Stochastically monotone Markov chains. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 10: 305–317.Google Scholar
Hu, T. & Joe, H. (1995). Monotonicity of positive dependence with time for stationary reversible Markov chains. Probability in the Engineering and Informational Sciences 9: 227–237.Google Scholar
Hu, T. & Pan, X. (2000). Comparisons of dependence for stationary Markov processes. Probability in the Engineering and Informational Sciences 14: 299–315.Google Scholar
Joe, H. (1997). Multivariate models and dependence concepts. London: Chapman & Hall.
Keilson, J. & Kester, A. (1977). Monotone matrices and monotone Markov processes. Stochastic Processes and Their Applications 5: 231–241.Google Scholar
Lindqvist, B.H. (1987). Monotone and associated Markov chains, with applications to reliability theory. Journal of Applied Probability 24: 679–695.Google Scholar
Marshall, A.W. & Olkin, I. (1979). Inequalities: Theory of majorization and its applications. New York: Academic Press.
Miyoshi, N. & Rolski, T. (2004). Ross type conjectures on monotonicity of queues. Australian & New Zealand Journal of Statistics 46: 121–131.Google Scholar
Müller A., &Stoyan, D. (2002). Comparison methods for stochastic models and risks. New York: Wiley.