General Mathematics


Ensuring Efficient Convergence to a Given Stationary Distribution

Authors: Kenny Peluso

How may we find a transition matrix that guarantees the long-run convergence of a Markov Chain to a given stationary distribution? Solving for this (usually) undetermined system is non-trivial and presents unique computational challenges. Five different of methods of directly solving for a transition matrix are presented along with their limitations. Relaxations of the two core assumptions underlying these direct methods - the Identityless and Independence Assumptions - are considered. A method of generating a Mass Matrix - the transition matrix underlying hops between entire population states - is described while developing the notion of successively-bounded weak compositions. An algorithm for their exhaustive generation is also presented. Applications of some methods are provided with respect to optimizing firm profit via optimally distributing workers among wage brackets and optimizing measures of national wealth via manipulation of class distribution and immigration policy. A generalization of all applications is formulated.

Comments: 29 Pages. Amended version of the author's undergraduate thesis, submitted 4/18

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Submission history

[v1] 2019-08-11 12:42:25

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