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Applications of positive definite kernels in probability

Grant number: 22/09840-0
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): September 01, 2022
Effective date (End): December 31, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Jean Carlo Guella
Grantee:Pedro Dragone Latini
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:21/04226-0 - Positive definite kernels applied to probability and statistics: MMD, HSIC and point process, AP.JP

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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