Approximating the solution of the chemical master equation by aggregation

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.