A limit theorem for the number of non-overlapping occurrences of a pattern in a sequence of independent trials
Ourania Chryssaphinou, Stavros G. Papastavridis · Journal of Applied Probability · 1988
A sequence of independent experiments is performed, each producing a letter from a given alphabet. Using a result by Barbour and Eagleson (1984) we prove that under general conditions the number of non-overlapping occurrences of long recurrent patterns has approximately a Poisson distribution.