# A Convex Approach to Steady State Moment Analysis for Stochastic Chemical Reactions

arXiv: https://arxiv.org/abs/1704.07722 · HTML: https://mlsanity.com/paper/1704.07722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Apr 2017.

## Built on by (most cited first, 1 of 1)

- [Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models](https://mlsanity.com/paper/2105.01536/) (2021)

## Abstract (arXiv)

Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. We show that the stochastic moments lie in a convex semi-algebraic set specified by linear matrix inequalities. Thus, the upper and the lower bounds of some moments can be computed by a semidefinite program. Using a protein dimerization process as an example, we demonstrate that the proposed method can precisely predict the mean and the variance of the copy number of the monomer protein.