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Some Applications, Properties and Conjectures for Higher Order Cumulants of a Markovian Stepping-Stone Model

Q. Zheng
J. Matis
Journal / Anthology

Communications in Statistics--Theory and Methods
Year: 1993
Volume: 22
Issue: 12
Page range: 3305-3319

This paper investigates certain tridiagonal coefficient matrices from linear differential equations for the joint cumulants of a Markovian stepping-stone model. The model is used to describe the dynamics of insect population growth, and is illustrated with an application to the spread of Africanized honey bees. The coefficient matrices are shown to have certain structure. A conjecture concerning their eigenvalues is proven for a special case of interest, and is also investigated numerically and by symbolic mathematical analysis.

*Mathematics > Calculus and Analysis > Differential Equations
*Mathematics > Probability and Statistics