Cumulative Bernoulli trials and Krawtchouk processes

AbstractA family of soluble Markov chains is introduced, which derive from simple prescriptions allowing ‘saved’ and ‘recouped’ successes in combinations of Bernoulli or hypergeometric trials. These processes lead directly to simple eigenvalue spectra and to eigenvectors which are classical polynomials of a discrete variable. A number of elementary, but apparently unrecognized, properties of ‘cumulative’ Bernoulli trials are discussed as background. Possible applications in epedemic and reliability theory are described