# Publications

## Citation

### BibTex format

@article{Kuntz:2017,author = {Kuntz, J and Thomas, P and Stan, G-B and Barahona, M},title = {Rigorous bounds on the stationary distributions of the chemical master  equation via mathematical programming},url = {http://arxiv.org/abs/1702.05468v1},year = {2017}}

### RIS format (EndNote, RefMan)

TY  - JOURAB  - The stochastic dynamics of networks of biochemical reactions in living cellsare typically modelled using chemical master equations (CMEs). The stationarydistributions of CMEs are seldom solvable analytically, and few methods existthat yield numerical estimates with computable error bounds. Here, we presenttwo such methods based on mathematical programming techniques. First, we usesemidefinite programming to obtain increasingly tighter upper and lower boundson the moments of the stationary distribution for networks with rationalpropensities. Second, we employ linear programming to compute convergent upperand lower bounds on the stationary distributions themselves. The boundsobtained provide a computational test for the uniqueness of the stationarydistribution. In the unique case, the bounds collectively form an approximationof the stationary distribution accompanied with a computable $\ell^1$-errorbound. In the non-unique case, we explain how to adapt our approach so that ityields approximations of the ergodic distributions, also accompanied withcomputable error bounds. We illustrate our methodology through two biologicalexamples: Schl\"ogl's model and a toggle switch model.AU  - Kuntz,JAU  - Thomas,PAU  - Stan,G-BAU  - Barahona,MPY  - 2017///TI  - Rigorous bounds on the stationary distributions of the chemical master  equation via mathematical programmingUR  - http://arxiv.org/abs/1702.05468v1ER  -