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Stochastic analysis of Bernoulli processes. (English) Zbl 1189.60089

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
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