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arXiv · 2212.00275

Unique Solutions to Power-Transformed Affine Systems

John Stachurski·Ole Wilms·Junnan Zhang
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Abstract

Systems of the form $x = (A x^s)^{1/s} + b$ arise in a range of economic, financial and control problems, where $A$ is a linear operator acting on a space of real-valued functions (or vectors) and $s$ is a nonzero real value. In these applications, attention is focused on positive solutions. We provide a simple and complete characterization of existence and uniqueness of positive solutions under conditions on $A$ and $b$ that imply positivity.

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John Stachurski, Ole Wilms, Junnan Zhang. 2022-12-01. Unique Solutions to Power-Transformed Affine Systems. https://arxiv.org/abs/2212.00275

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