Maxentropic Markov chains

It is well known that random walks and similar Markov chains [l] can be used as approximations for or analogs to Brownian motion or diffusion which are more precisely described by continuous stochastic processes. In cormection with digital system analysis it is also desirable to have Markov chains, which approximate continuous processes with finite variance [2], [3]. Moreover, it is an important result in information theory [4] that Gauss-Markov processes have maximum entropy among all processes with given values of the first and second moments. Another application of maxentropic Markov chains appears in [5]. In [6] the maxentropic Markov chain was used in the derivation of an upper bound to the entropy of certain spectrum shaping codes.