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


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.


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Nicolas Privault. "Stochastic analysis of Bernoulli processes." Probab. Surveys 5 435 - 483, 2008.


Published: 2008
First available in Project Euclid: 29 December 2008

zbMATH: 1189.60089
MathSciNet: MR2476738
Digital Object Identifier: 10.1214/08-PS139

Primary: 60G42 , 60G42 , 60G50 , 60G51 , 60H07 , 60H30
Secondary: 60G42

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

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.5 • 2008
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