title: Exact results in the large system size limit for the dynamics of the chemical master equation, a one dimensional chain of equations.
abstract: 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 the Van Kampen method from the HJE approach using a special ansatz. Using the Van Kampen method, we give a system of ordinary differential equations (ODEs) to define the variance in a two-dimensional case. We performed numerics for the CME with stationary noise. We give analytical criteria for the disappearance of bistability in the case of stationary noise in one-dimensional CMEs.
authors.affiliation: Yerevan State University, Alex Manoogian 1, Yerevan 375025, Armenia.
authors.forename: A
authors.initials: A
authors.lastname: Martirosyan
authors.forename: David B
authors.initials: DB
authors.lastname: Saakian
mesh_terms: D004548:Elasticity; D008956:Models, Chemical; D011336:Probability