# Malliavin calculus

May 23, 2020 — May 25, 2020

dynamical systems

SDEs

signal processing

stochastic processes

time series

You can calculate a derivative of densities for stochastic processes in some generalised sense which I do not at present understand, and do the normal calculus thing you do with a derivative. Stochastic differential equations arise, presumably ones in some sense involving this generalised derivative, can then solve some kind of problems for you. Or something.

Clearly this is a placeholder for a topic I do not have time for right now. 🏗

## 1 References

Bell. 2006.

*The Malliavin Calculus*.
Bichteler, Gravereaux, and Jacod. 1987.

*Malliavin Calculus for Processes with Jumps*. Stochastics Monographs, v. 2.
Di Nunno, Øksendal, and Proske. 2009.

*Malliavin Calculus for Lévy Processes with Applications to Finance*. Universitext.
Friz. 2005. “An Introduction to Malliavin Calculus.”

Levajkovic, and Selesi. 2011. “Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative, Part I.”

*Publications de l’Institut Mathematique*.
Nualart. 2006.

*The Malliavin Calculus and Related Topics*. Probability and Its Applications.
Øksendal. 1997.

*An Introduction to Malliavin Calculus with Applications to Economics*.
Osswald. 2012.

*Malliavin Calculus for Lévy Processes and Infinite-Dimensional Brownian Motion: An Introduction*. Cambridge Tracts in Mathematics 191.
Sanz-Solé. 2004.

*A Course on Malliavin Calculus*.
Schiller. 2009. “Malliavin Calculus for Monte Carlo Simulation with Financial Applications.”

Zhang. 2004. “The Malliavin Calculus.”