1212.1539 (Arax Martirosyan et al.)

Exact results in the large system size limit for the dynamics of the
Chemical Master Equation, a one dimensional chain of equations    [PDF]

Arax Martirosyan, David B. Saakian

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.

View original: http://arxiv.org/abs/1212.1539