Formulas on Orthogonal Functionals of Stochastic Binary Sequence

摘要

This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking ±1 with equal probability. Several mathematical formulas, such as multi-variate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A simple example of orthogonal functional expansion and stationary random sequence generated by the stationary binary sequence are discussed.