## Ergodicity analysis and antithetic integral control of a class of stochastic reaction networks with delays. (arXiv:1811.09188v1 [math.OC])

Delays are an important phenomenon arising in a wide variety of real world
systems. They occur in biological models because of diffusion effects or as
simplifying modeling elements. We propose here to consider delayed stochastic
reaction networks. The difficulty here lies in the fact that the state-space of
a delayed reaction network is infinite-dimensional, which makes their analysis
more involved. We demonstrate here that a particular class of stochastic
time-varying delays, namely those that follow a phase-type distribution, can be
exactly implemented in terms of a chemical reaction network. Hence, any
delay-free network can be augmented to incorporate those delays through the
addition of delay-species and delay-reactions. Hence, for this class of
stochastic delays, which can be used to approximate any delay distribution
arbitrarily accurately, the state-space remains finite-dimensional and,
therefore, standard tools developed for standard reaction network still apply.
In particular查看全文