ON CONSECUTIVE RECORDS IN CERTAIN BERNOULLI SEQUENCES

• In an infinite sequence of independent Bernoulli trials with success probabilities p(k) = a/(a + b + k - 1) for k = 1, 2 3, ... , let N-r be the number of r >= 2 consecutive successes. Expressions for the first two moments of N-r are derived. Asymptotics of the probability of no occurrence of r consecutive successes for large r are obtained. Using an embedding in a marked Poisson process, it is indicated how the distribution of N-r can be calculated for small r.

Nyckelord

Bernoulli trial

embedding in Poisson process

random permutation

records

runs of successes

sums of indicators

poisson processes

number

strings

counts

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