Stochastic analysis of Bernoulli processes
Probability
2018-06-04 v3
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.
Cite
@article{arxiv.0809.3168,
title = {Stochastic analysis of Bernoulli processes},
author = {Nicolas Privault},
journal= {arXiv preprint arXiv:0809.3168},
year = {2018}
}
Comments
Originally published in at http://dx.doi.org/10.1214/08-PS139 the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org) This version includes a revision of Section 9