On the solutions and the steady states of a master equation
Abstract
A complete characterization of the time behavior of the means and variance of a stochastic process which is generated by a finite number of independent systems is presented based on the master equation for the conditional probability. It is found that the means and variance relax to a steady state and that the steady state will be independent of the initial state if and only if a matrix related to the transition matrix is nonsingular. Finally, the result that the variance approaches its steady-state form at twice the rate of the means is shown to depend on the nonsingularity of the same matrix.
- Publication:
-
Journal of Statistical Physics
- Pub Date:
- November 1972
- DOI:
- 10.1007/BF01023679
- Bibcode:
- 1972JSP.....6...67K
- Keywords:
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- Master equation;
- stochastic process;
- steady states