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Stochastic analysis of Bernoulli processes
Nicolas Privault
Source: Probab. Surveys Volume 5 (2008), 435-483.
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.
Primary Subjects: 60G42, 60G42, 60G50, 60G51, 60H30, 60H07
Secondary Subjects: 60G42
Keywords: Malliavin calculus; Bernoulli processes; discrete time; chaotic calculus; functional inequalities; option hedging
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ps/1230559281
Digital Object Identifier: doi:10.1214/08-PS139
Mathematical Reviews number (MathSciNet):
MR2476738
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