Approximating the solution of the chemical master equation by aggregation

Markus Hegland

Abstract


The chemical master equation is a continuous time discrete space Markov model of chemical reactions. The chemical master equation is derived mathematically and it is shown that the corresponding initial value problem has a unique solution. Conditions are given under which this solution is a probability distribution. We present finite state and aggregation-disaggregation approximations and provide error bounds for the case of piecewise constant disaggregation. The aggregation-disaggregation approximation allows the solution of the chemical master equation for larger state spaces and is also an important tool for the solution of multidimensional problems.

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DOI: http://dx.doi.org/10.21914/anziamj.v50i0.1426



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