# Abstraction-Guided Truncations for Stationary Distributions of Markov Population Models

arXiv: https://arxiv.org/abs/2105.01536 · HTML: https://mlsanity.com/paper/2105.01536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 49 references that are in the map.
- First posted on arXiv 3 May 2021.

## Builds on (most cited first, 5 of 5)

- [A scalable computational framework for establishing long-term behavior of stochastic reaction networks](https://mlsanity.com/paper/1304.5404/) (2013)
- [A Convex Approach to Steady State Moment Analysis for Stochastic Chemical Reactions](https://mlsanity.com/paper/1704.07722/) (2017)
- [Semi-Quantitative Abstraction and Analysis of Chemical Reaction Networks](https://mlsanity.com/paper/1905.09914/) (2019)
- [Stationary distributions of continuous-time Markov chains: a review of theory and truncation-based approximations](https://mlsanity.com/paper/1909.05794/) (2019)
- [Analysis of Markov Jump Processes under Terminal Constraints](https://mlsanity.com/paper/2010.10096/) (2020)

## Abstract (arXiv)

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine relevant and truncate irrelevant parts of the state-space. This way, the algorithm learns a well-justified finite-state projection tailored to the stationary behavior. We demonstrate the method's applicability to a wide range of non-linear problems with complex stationary behaviors.