Probability Surveys

Stochastic analysis of Bernoulli processes

Nicolas Privault

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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.

Article information

Source
Probab. Surveys, Volume 5 (2008), 435-483.

Dates
First available in Project Euclid: 29 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.ps/1230559281

Digital Object Identifier
doi:10.1214/08-PS139

Mathematical Reviews number (MathSciNet)
MR2476738

Zentralblatt MATH identifier
1189.60089

Subjects
Primary: 60G42: Martingales with discrete parameter 60G42: Martingales with discrete parameter 60G50: Sums of independent random variables; random walks 60G51: Processes with independent increments; Lévy processes 60H30: Applications of stochastic analysis (to PDE, etc.) 60H07: Stochastic calculus of variations and the Malliavin calculus
Secondary: 60G42: Martingales with discrete parameter

Keywords
Malliavin calculus Bernoulli processes discrete time chaotic calculus functional inequalities option hedging

Citation

Privault, Nicolas. Stochastic analysis of Bernoulli processes. Probab. Surveys 5 (2008), 435--483. doi:10.1214/08-PS139. https://projecteuclid.org/euclid.ps/1230559281


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