Malliavin Calculus and Applications

Basic information

Workload: 

45 hours

Prerequisite: 

Measure, Integration and Probability, Stochastic Calculation, Functional Analysis: Fundamentals, Functional Analysis: Linear Operators 

Syllabus: 

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.

Bibliography

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.