Applications of positive definite kernels in probability

• Grant number: 22/09840-0
• Support Opportunities: Scholarships in Brazil - Master
• Start date: September 01, 2022
• End date: 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.