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Guided simulation of conditioned chemical reaction networks

Marc Corstanje & Frank van der Meulen

Statistical Inference for Stochastic Processes2025https://doi.org/10.1007/s11203-025-09326-9article
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What the paper says

Let <i>X</i> be a chemical reaction process, modeled as a multi-dimensional continuous-time jump process. Assume that at given times <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:msub><mml:mi>t</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo><</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo><</mml:mo> <mml:msub><mml:mi>t</mml:mi> <mml:mi>n</mml:mi></mml:msub> </mml:mrow> </mml:math> , linear combinations <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>v</mml:mi> <mml:mi>i</mml:mi></mml:msub> <mml:mo>=</mml:mo> <mml:msub><mml:mi>L</mml:mi> <mml:mi>i</mml:mi></mml:msub> <mml:mi>X</mml:mi> <mml:mrow><mml:mo>(</mml:mo> <mml:msub><mml:mi>t</mml:mi> <mml:mi>i</mml:mi></mml:msub> <mml:mo>)</mml:mo></mml:mrow> <mml:mo>,</mml:mo> <mml:mspace></mml:mspace> <mml:mi>i</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi></mml:mrow> </mml:math> are observed for given matrices <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>L</mml:mi> <mml:mi>i</mml:mi></mml:msub> </mml:math> . We show how the process that is conditioned on hitting the states <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:msub><mml:mi>v</mml:mi> <mml:mn>1</mml:mn></mml:msub> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:msub><mml:mi>v</mml:mi> <mml:mi>n</mml:mi></mml:msub> </mml:mrow> </mml:math> 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.

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https://doi.org/https://doi.org/10.1007/s11203-025-09326-9

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@article{marc2025,
  title        = {{Guided simulation of conditioned chemical reaction networks}},
  author       = {Marc Corstanje & Frank van der Meulen},
  journal      = {Statistical Inference for Stochastic Processes},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1007/s11203-025-09326-9},
}

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Guided simulation of conditioned chemical reaction networks

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F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
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R · text relevance †0.50 × 0.4 = 0.20

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