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.

Basic Information

Workload
45 hours
Requirements
Measure, Integration and Probability, Stochastic Calculation, Functional Analysis: Fundamentals, Functional Analysis: Linear Operators

Mandatory: 

  • 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.

Complementary

  • 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.