1. Discrete chaotic calculus and covariance identities.
- Author
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Privault, Nicolas and Schoutens, Wim
- Subjects
- *
MARKOV processes , *POLYNOMIALS - Abstract
We show that for the binomial process (or Bernoulli random walk) the orthogonal functionals constructed in Kroeker, J.P. (1980) "Wiener analysis of functionals of a Markov chain: application to neural transformations of random signals", Biol. Cybernetics 36 , 243-248, [14] for Markov chains can be expressed using the Krawtchouk polynomials, and by iterated stochastic integrals. This allows to construct a chaotic calculus based on gradient and divergence operators and structure equations, and to establish a Clark representation formula. As an application we obtain simple infinite dimensional proofs of covariance identities on the discrete cube. [ABSTRACT FROM AUTHOR]
- Published
- 2002
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