Journal of Applied Mathematics and Decision Sciences
Volume 4 (2000), Issue 1, Pages 39-64
A coupling technique for stochastic comparison of functions of Markov Processes
ENSEEIHT, 2 rue Camichel, Toulouse 31071, France
Copyright © 2000 M. Doisy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The aim of this work is to obtain explicit conditions (i.e., conditions on the transition
rates) for the stochastic comparison of Markov Processes. A general coupling technique is used
to obtain necessary and sufficient conditions for the construction of a coupling Markov Process
which stays in a fixed set for all times and with given marginal processes. The strong stochastic
comparison—or, more generally, the stochastic comparison through states functions—appears as
a particular case. An example in the Reliability Theory is developed and proves the efficiency
of the method. Systems with multiple component types and redundant units are stochastically
compared directly or through particular functions.