# Analysis of Markov Jump Processes under Terminal Constraints

arXiv: https://arxiv.org/abs/2010.10096 · HTML: https://mlsanity.com/paper/2010.10096/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Oct 2020.

## 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)

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme that aggregates states in a grid structure. The resulting approximate bridging 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 yielding guaranteed lower bounds for the system behavior under endpoint constraints. We demonstrate the method's applicability to a wide range of problems such as Bayesian inference and the analysis of rare events.