Abstract
These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable representation, anticipating calculus, covariance identities and functional inequalities (such as deviation and logarithmic Sobolev inequalities), and an application to option hedging in discrete time.
| Original language | English |
|---|---|
| Pages (from-to) | 435-483 |
| Journal | Probability Surveys |
| Volume | 5 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2008 |
Research Keywords
- Bernoulli processes
- chaotic calculus
- discrete time
- functional inequalities
- Malliavin calculus
- option hedging
Publisher's Copyright Statement
- This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/