Generating functions in Riesz spaces
Youssef Azouzi, Youssef Nasri
TL;DR
This paper introduces generating functions for natural elements in Dedekind complete Riesz spaces with conditional expectation, enabling the analysis of discrete processes and improving Poisson approximation results.
Contribution
It develops the concept of generating functions in Riesz spaces, advancing the mathematical framework for studying discrete processes in this setting.
Findings
Enhanced Poisson approximation results
New framework for generating functions in Riesz spaces
Application to discrete process analysis
Abstract
We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectatnion operator. This allows to study discrete processes in free-measure setting. In particular we improve a result obtained by Kuo, Vardy and Watson concerning Poisson approximation.
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Taxonomy
TopicsAdvanced Banach Space Theory · Stochastic processes and financial applications · Advanced Harmonic Analysis Research