Stochastic analysis of Bernoulli processes

Details Stochastic analysis of Bernoulli processes Stochastic analysis of Bernoulli processes

2008-09-18

arxiv.org/abs/0809.3168v2

Probability Surveys 2008, Vol. 5, 435-483

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/08-PS139 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of

Scientific paper

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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