Versik processes: First steps

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A. M. Versik defined a property of finite-state stationary stochastic processes that formally is slightly weaker than D. S. Ornstein’s very weak Bernoulli (VWB) property. Versik conjectured his property was equivalent withVWB. The conjecture is false. We construct a zero entropy Versik process that is not loosely Bernoulli (LB) and, by taking a skew product of this process with the two-shift, we produce aK process that is Versik but notVWB. Our technique for constructing a non-LB process differs from the few known methods.