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Discrete chaotic calculus and covariance identities.
- Source :
-
Stochastics & Stochastics Reports . Apr2002, Vol. 72 Issue 3/4, p289. 28p. - Publication Year :
- 2002
-
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]
- Subjects :
- *MARKOV processes
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 10451129
- Volume :
- 72
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Stochastics & Stochastics Reports
- Publication Type :
- Academic Journal
- Accession number :
- 10955585
- Full Text :
- https://doi.org/10.1080/10451120290019230