  We apply the Hamilton-Jacobi equation (HJE) formalism to solve the dynamics
of the Chemical Master Equation (CME). We found exact analytical expressions
(in large system-size limit) for the probability distribution, including
explicit expression for the dynamics of variance of distribution. We also give
the solution for some simple cases of the model with time-dependent rates. We
derived the results of Van Kampen method from HJE approach using a special
ansatz. Using the Van Kampen method, we give a system of ODE to define the
variance in 2-d case. We performed numerics for the CME with stationary noise.
We give analytical criteria for the disappearance of bi-stability in case of
stationary noise in 1-d CME.
