A Study of Counts of Bernoulli Strings via Conditional Poisson Processes

@inproceedings{Huffer2008ASO,
  title={A Study of Counts of Bernoulli Strings via Conditional Poisson Processes},
  author={Fred W. Huffer and Jayaram Sethuraman and Sunder Sethuraman},
  year={2008}
}
A sequence of random variables, each taking values 0 or 1, is called a Bernoulli sequence. We say that a string of length d occurs, in a Bernoulli sequence, if a success is followed by exactly (d − 1) failures before the next success. The counts of such d-strings are of interest, and in specific independent Bernoulli sequences are known to correspond to asymptotic dcycle counts in random permutations. In this note, we give a new framework, in terms of conditional Poisson processes, which allows… CONTINUE READING