An Itô-Ventzell type formula for Hölder paths

Author(s)

Rafael Andretto Castrequini

• Document type: Doctoral Thesis
• Press: Campinas, SP.
• Institution: Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica
• Defense date: 2014-09-19

Examining board members

Pedro Jose Catuogno; Christian Horacio Olivera; Luiz Antonio Barrera San Martin; Osvaldo Germano do Rocio; Alberto Masayoshi Faria Ohashi

• Advisor: Pedro Jose Catuogno

Abstract

We prove an Itô-Ventezel type formula for Hölder paths with exponent is greater than 1/3. The most important class of examples of theses paths is given by fractional Brownian motion. Our formula is an extension (and agree) to classic version done by H. Kunita in 80's. The technical tools used rely on rough path theory following M. Gubinelli's approach. Those techniques were developed in the late 90's. by T. Lyons. As an application, we study differential equations driven by paths with exponent greater than 1/2 (Young Systems). The ideia here is to employ our formula together with method of characteristics in this setting, following Kunita's work (AU)

• FAPESP's process: 09/11430-0 - Stochastic calculus, rough paths and stochastic equations.
• Grantee: Rafael Andretto Castrequini
• Support Opportunities: Scholarships in Brazil - Doctorate