A note on harmonic continuation of characteristic function
Saulius Norvidas
TL;DR
This paper establishes a precise criterion using harmonic and completely monotonic functions to determine when a real-valued function on the real line is a characteristic function of a probability measure.
Contribution
It provides a necessary and sufficient condition for characteristic functions based on harmonic and monotonic function properties, advancing theoretical understanding.
Findings
Characterizes characteristic functions via harmonic functions.
Links harmonic and completely monotonic functions to probability measures.
Offers a complete criterion for identifying characteristic functions.
Abstract
We propose a necessary and sufficient condition for a real-valued function on the real line to be a characteristic function of a probability measures. The statement is given in terms of harmonic functions and completely monotonic functions.
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Taxonomy
TopicsStochastic processes and financial applications · Statistical Mechanics and Entropy · Bayesian Methods and Mixture Models