Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2025-01-03T21:20:13.230Z Has data issue: false hasContentIssue false
  • English
  • Français

Some results on Markovian replacement processes

Published online by Cambridge University Press:  14 July 2016

Petr Mandl
Petr Mandl*
Affiliation:
University of Manchester
*
* Permanent address: Czechoslovak Academy of Sciences, Institute of Information Theory and Automation, Prague.
Get access Rights & Permissions [Opens in a new window]

Summary

A replacement of type (jk) in a Markov process with rewards means an instantaneous shift of the trajectory from state j into state k. A formula is obtained for the characteristic function of the total reward from the process under an arbitrary non-anticipative replacement policy. From the formula results are deduced concerning Markov policies, optimal policies and policies minimizing the variance of the reward.

Type
Research Papers
Information
Journal of Applied Probability , Volume 8 , Issue 2 , June 1971 , pp. 357 - 365
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

[1] Derman, C. (1963) Optimal replacement and maintenance under Markovian deterioration with probability bounds on failure. Management Sci. 9, 478–481.CrossRefGoogle Scholar
[2] Howard, R. A. (1960) Dynamic Programming and Markov Processes. M.I.T. Press and John Wiley, New York and London.Google Scholar
[3] Mandl, P. (1969) An identity for Markovian replacement processes. J. Appl. Prob. 6, 348–354.CrossRefGoogle Scholar