%0 Journal Article
%T An exact reduction of the master equation to a strictly stable system with an explicit expression for the stationary distribution
%A Daniel Soudry
%A Ron Meir
%J Quantitative Biology
%D 2012
%I arXiv
%X The evolution of a continuous time Markov process with a finite number of states is usually calculated by the Master equation - a linear differential equations with a singular generator matrix. We derive a general method for reducing the dimensionality of the Master equation by one by using the probability normalization constraint, thus obtaining a affine differential equation with a (non-singular) stable generator matrix. Additionally, the reduced form yields a simple explicit expression for the stationary probability distribution, which is usually derived implicitly. Finally, we discuss the application of this method to stochastic differential equations.
%U http://arxiv.org/abs/1207.4436v1