Stochastic analysis of Bernoulli processes

By Nicolas Privault. 2008

77 citations recorded by the source corpus.

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.

Subfields: Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/70076adb78fc7d45833d57e31070a206b2fe0ac0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

1. Ivan Nourdin
2. Giovanni Peccati
3. Gesine Reinert
4. Nicolas Privault
5. David Nualart
6. Frederi G. Viens
7. Ciprian A. Tudor
8. Michel Ledoux

In Statistical and Nonlinear Physics

1. Ivan Nourdin
2. Giovanni Peccati
3. Gesine Reinert
4. Mark Newman

Citations in the corpus

• Stein's method meets Malliavin calculus: a short survey with new estimates (2009, background): “[21℄ I. Nourdin, G. Pe ati and G. Reinert (2008).”
• Stein's Method and Stochastic Analysis of Rademacher Functionals (2008, methodology): “In [5], Chatterjee proves that, in Wasserstein distance, Note that max and due e.g. to (2.5), Relation (4.46) gives an alternate proof of the implication (b) → (a) in Proposition 4.6.”
• Stochastic Analysis in Discrete and Continuous Settings: With Normal Martingales (2009, background): “This chapter is a revision of [117] with some additions, and is mainly based on [61] and [119].”