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arXiv · 1207.4436

An exact reduction of the master equation to a strictly stable system with an explicit expression for the stationary distribution

Daniel Soudry·Ron Meir
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Abstract

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.

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Daniel Soudry, Ron Meir. 2012-07-18. An exact reduction of the master equation to a strictly stable system with an explicit expression for the stationary distribution. https://arxiv.org/abs/1207.4436

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