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 Probability Surveys > Vol. 5 (2008) open journal systems 

Stochastic analysis of Bernoulli processes

Nicolas Privault, City University of Hong Kong

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.

AMS 2000 subject classifications: Primary 60G42, 60G42, 60G50, 60G51, 60H30, 60H07; secondary 60G42.

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

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Privault, Nicolas, Stochastic analysis of Bernoulli processes, Probability Surveys, 5, (2008), 435-483 (electronic). DOI: 10.1214/08-PS139.


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