Th e problem of d ec iding wh e n a st.ationary stocha sti c process is a function of a finit e Markov process has bee n con s id e re d by se ve ral au thors, leading t.o an elegant necessary and s uffi c ie nt. cond ition. Taking a diffe re nt approac h , t.hi s not.e uses ele me nt a ry ring th eory to prove that a ce rtain e xp li c itly constru c te d st.ationary e rgod ic process is not. a functi on of any finit e Ma rk ov process. Ke y word s : In formati on t.h eory; Markov process;

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... ability th eory; rin g th eory; st.oc has ti c process. * He lpful di sc uss ions with A. J. Go ldm an, J. Le vy and M. Newman a re grat efully ac knowle dge d. ** Nati onal Bureau of S tandard s and Unive rs ity of P e nns ylvania Medical Sc hool. I Fi gures in bracket s indi cat e th e literature referen ces at the end of thi s paper. 133 (1.1)