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Updated: May 29, 2025

Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics BM-PROMA
Published on: August 28, 2021
On sociologically derived mathematics
1Emerging Pathogens Institute, University of Florida, P.O. Box 100009, Gainesville, FL 32610, USA.
Abstract:
Motivated by empirical studies of labor mobility, in 1970 Sy Spilerman approached me with a question about when a given stochastic matrix, P, can be reached from the identity matrix, I, in a prescribed period of time via the Kolmogorov forward and backward differential equations. A complete answer to this question for time-homogeneous Markov chains was provided in 1976-summarized herein-and a diversity of time-inhomogeneous cases have been studied since then and are reviewed in the present paper. Of particular interest for the future would be solutions for this reachability/embedding problem for mixtures of Markov chains. Also for the future would be studies of partial identifiability of mixtures of Markov chains when their observed transitions do not satisfy reachability/embedding conditions.
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