Mathematics – Probability
Scientific paper
2011-12-13
Mathematics
Probability
Scientific paper
We consider the invariant measure of a homogeneous continuous- time Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geo- metric distribution. Second, we show that a countable linear combina- tion of geometric terms can be an invariant measure only if it consists of pairwise-coupled terms. As a consequence, we obtain a complete characterization of all countable linear combinations of geometric dis- tributions that may yield an invariant measure for a homogeneous continuous-time Markov process in the quarter-plane.
Boucherie Richard J.
Chen Yanting
Goseling Jasper
No associations
LandOfFree
The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-486846