论文信息 - One‐dimensional chemical master equations: Uniqueness and analytical form of certain solutions

One‐dimensional chemical master equations: Uniqueness and analytical form of certain solutions

The eikonal (WKB) approximation is applied to a stationary one‐dimensional master equation describing an arbitrary reaction mechanism. The uniqueness of a nontrivial (fluctuational) eikonal solution is proven. Consistent eikonal and exact analytical solutions are obtained for systems with an arbitrary, but unique step size of stochastic transitions. An analytical eikonal solution for the stationary probability density for systems with mixed step sizes of 1 and 2 is also obtained and found to differ significantly from the systems with a uniform step size, particularly in the case of multiple stationary states.

Michael S. Samoilov | J. Ross | M. Samoilov | John Ross

[1] N. Kampen,et al. Stochastic processes in physics and chemistry , 1981 .

[2] Mark Dykman,et al. Large fluctuations and optimal paths in chemical kinetics , 1994 .

[3] C. Gardiner. Handbook of Stochastic Methods , 1983 .

[4] D. Gillespie. A rigorous derivation of the chemical master equation , 1992 .

[5] S. Orszag,et al. Advanced Mathematical Methods For Scientists And Engineers , 1979 .

[6] P. M. Hunt,et al. Thermodynamics far from equilibrium: Reactions with multiple stationary states , 1988 .

[7] D. Gillespie. Markov Processes: An Introduction for Physical Scientists , 1991 .

[8] Granino A. Korn,et al. Mathematical handbook for scientists and engineers , 1961 .

[9] Joel Keizer,et al. Statistical Thermodynamics of Nonequilibrium Processes , 1987 .