Computing the solution of the chemical master equation is qualitatively the best option available when investigating the dynamics of many cellular processes, because due to the low molecule copy numbers present in such networks, inherent stochastic fluctuations can significantly influence the results. However, solving the chemical master equation numerically is often impossible due to the high-dimensional space associated with this equation. In this talk, we present a way to mitigate the effects of the curse of dimensionality by using wavelet compression. In order to achieve further reductions
in the number of degrees of freedom required to approximate the solution, the adaptive wavelet method for the chemical master equation is embedded within a hybrid strategy. The main idea is to use the computationally intensive wavelet approach only for the parts of the biochemical reaction networks composed of species with small concentrations and treat the remaining components in a deterministic setting. The stationary solution of the chemical master equation for the full system is computed by alternately calling the adaptive wavelet method for the stochastic part, and a Newton method for the deterministic description. This approach allows for the numerical treatment of systems with large state spaces. Numerical results to illustrate the potential of the method and further development are also discussed.