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Applications of positive definite kernels in probability

Grant number: 23/14442-7
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): February 01, 2024
Effective date (End): August 31, 2024
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Paulo Regis Caron Ruffino
Grantee:Pedro Dragone Latini
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project aims to study recent results in the literature about the connection between positive definite kernels and concepts from probability, such as metrics in this space, independence and conditional independence. For this purpose, it is used the reproducing kernel Hilbert space of a positive definite kernel in order to obtain a semi-inner product on the space of measures with bounded variation. In order to obtain examples and characterization of certain types of kernels, it is analyzed the strong relation between positive definite kernels and harmonic analysis.

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