Malliavin Calculus and Applications

Wiener space, isonormal Gaussian process, Wiener chaos decomposition, Malliavin derivative, divergence operator, the Skorohod integral, white noise. Ornstein-Uhlenbeck semigroup. Regularity of probability laws, hypoellipticity and Hörmander Theorem. Applications to fractional Brownian motion and Financial Mathematics.

Informações Básicas

Carga horária
45 horas
Pré-requisito
Medida, Integração e Probabilidade, Cálculo Estocástico, Análise Funcional: Fundamentos, Análise Funcional: Operadores Lineares

Obrigatória: 

  • Nualart (2006). The Malliavin Calculus and Related Topics. Springer
  • Malliavin, Thalmaier (2006). Stochastic Calculus of Variations in Mathematical Finance. Springer.
  • Di Nunno, Oksendal, Proske (2008). Malliavin Calculus for Lévy Processes with Applications to Finance. Springer.

Complementar: 

  • Bell (2006). The Malliavin Calculus. Dover.
  • Viens, Feng, Hu, Nualart (2013). Malliavin Calculus and Stochastic Analysis. Springer.
  • Levajković, Mena (2017). Equations Involving Malliavin Calculus Operators. Springer.
  • Da Prato (2008).  Introduction to Stochastic Analysis and Malliavin Calculus. Springer.
  • Malliavin (1997). Stochastic Analysis. Springer.