Minimal order for transience in a closed class among endotactic stochastic mass‑action systems

Determine the minimal reaction order k for which there exists an endotactic stochastic mass‑action system of order k whose continuous‑time Markov chain is transient within a closed communicating class.

Background

While the paper provides broad non-explosivity results for second‑order endotactic systems, recurrence properties can still fail for higher orders. A known strongly endotactic example of order 7 exhibits transience.

The precise threshold order at which transience first becomes possible for endotactic stochastic mass-action systems restricted to a closed communicating class remains undetermined.

References

In , a 7th order transient strongly endotactic stochastic mass-action system was constructed. The author is unaware of what is the minimal order for an endotactic stochastic mass-action system to be transient in a closed communicating class.

— Non-explosivity of endotactic stochastic reaction systems (2409.05340 - Xu, 9 Sep 2024) in Remark (Section 3, Non-explosivity) following the example on transience