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Asymptotics and Criticality for a Correlated Bernoulli Process

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A generalized binomial distribution that was proposed by Drezner & Farnum in 1993 comes from a correlated Bernoulli process with interesting asymptotic properties which differ strikingly in the neighbourhood of a critical point. The basic asymptotics and a short-range/long-range dependence dichotomy are presented in this note.
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Keywords: asymptotics; correlated Bernoulli process; critical value; generalized binomial; long-range dependence; martingales

Document Type: Research Article

Affiliations: Mathematical Sciences Institute, The Australian National University, Canberra, Australia

Publication date: March 1, 2004

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