preprintZenodo (CERN European Organization for Nuclear Research)Mar 13, 2026GREEN OA

Spectral Mean Flow and Variance Dynamics of Completely Monotone Functions

LMLouis Morissette

Université Sainte-Anne

Indexed indatacite

Abstract

[English] We study functions representable as finite positive mixtures of exponential modes, F(t) = sum_k a_k exp(-lambda_k t), and their associated effective rate r(t) = -F'(t)/F(t). We prove four exact results. (1) A universal variance identity: r'(t) = -Var_t(lambda)

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Topics & keywords

Topics
Keywords
  • Exponential function
  • Measure (data warehouse)
  • Monotonic function
  • Quadratic equation
  • Exponential polynomial
  • Monotone polygon
  • Dynamical systems theory
  • Natural exponential family
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