Stochastic analysis of Bernoulli processes. (English) Zbl 1189.60089

Privault, Nicolas

Probab. Surv. 5, 435-483 (2008).

Summary: 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.

MSC:

60G42	Martingales with discrete parameter
60G50	Sums of independent random variables; random walks
60G51	Processes with independent increments; Lévy processes
60H30	Applications of stochastic analysis (to PDEs, etc.)
60H07	Stochastic calculus of variations and the Malliavin calculus
91G80	Financial applications of other theories
60-02	Research exposition (monographs, survey articles) pertaining to probability theory

Keywords:

Malliavin calculus; Bernoulli processes; discrete time; chaotic calculus; functional inequalities; option hedging