REVIEW
The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
The Invariant Measure of Homogeneous Markov Processes in The Quarter-Plane: Representation in Geometric Terms
read the original abstract
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.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.