# Guided simulation of conditioned chemical reaction networks

## TL;DR

This paper introduces a method to simulate chemical reactions under specific conditions using mathematical transformations.

## Contribution

The novelty is deriving an algorithm for simulating conditioned chemical reaction processes via a change of measure.

## Key findings

- A mathematical framework is developed to condition chemical reaction processes on observed states.
- The proposed algorithm generates weighted samples from the conditioned process.
- Numerical simulations validate the effectiveness of the approach.

## Abstract

Let X be a chemical reaction process, modeled as a multi-dimensional continuous-time jump process. Assume that at given times \documentclass[12pt]{minimal}
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\begin{document}$$0< t_1< \cdots <t_n$$\end{document}0<t1<⋯<tn, linear combinations \documentclass[12pt]{minimal}
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\begin{document}$$v_i = L_i X(t_i),\, i=1,\dots ,n$$\end{document}vi=LiX(ti),i=1,⋯,n are observed for given matrices \documentclass[12pt]{minimal}
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\begin{document}$$L_i$$\end{document}Li. We show how the process that is conditioned on hitting the states \documentclass[12pt]{minimal}
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\begin{document}$$v_1,\dots , v_n$$\end{document}v1,⋯,vn is obtained by a change of measure on the law of the unconditioned process. This results in an algorithm for obtaining weighted samples from the conditioned process. Our results are illustrated by numerical simulations.