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Comportement asymptotique des marches aleatoires associees aux polynomes de Gegenbauer et applications
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- Journal:
- Advances in Applied Probability / Volume 16 / Issue 2 / June 1984
- Published online by Cambridge University Press:
- 01 July 2016, pp. 293-323
- Print publication:
- June 1984
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- Article
- Export citation
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Random walks on N associated with orthogonal polynomials have properties similar to classical random walks on
. In fact such processes have independent increments with respect to a hypergroup structure on 
with a convolution and a Fourier transform which is the basic tool for their study. We illustrate these ideas by giving a description of the asymptotic behaviour (CLT and ILL) of the random walks associated with Gegenbauer's polynomials. Moreover we can then use these random walks as a reference scale to deduce asymptotic properties of other Markov chains on 
via a comparison theorem which is of independent interest.
. In fact such processes have independent increments with respect to a hypergroup structure on 
with a convolution and a Fourier transform which is the basic tool for their study. We illustrate these ideas by giving a description of the asymptotic behaviour (CLT and ILL) of the random walks associated with Gegenbauer's polynomials. Moreover we can then use these random walks as a reference scale to deduce asymptotic properties of other Markov chains on 
via a comparison theorem which is of independent interest.