Decomposing Statistical Periodicities

Nonstationary random symbolic sequences are investigated for cyclostationarity and decomposition into constituent cyclostationary sources. Since the symbolic sources do not admit an algebraic structure, a composition of distributions of cyclostationary sources is studied that models the erosion in symbolic sequences, for instance, mutations in gene sequences. This composition gives a rich mathematical structure on the collection of cyclostationary sources and a uniqueness theorem for decomposition of pq-statistically periodic symbolic sources into cyclostationary sources with periods p and q, when p and q are coprime.