Remarks on a Markov chain example of Kolmogorov

Summary It is shown that the stochastic transition matrix P(t), in Kolmogorov's example of a process with an instantaneous state, is uniquely determined by the derivative matrix Q=P(0), and the most general such substochastic P(t) is also found. The example is used to show that, if 0 is an instantaneous state, then 1-p ₀₀(t) can tend to 0 arbitrarily slowly and on the other hand (1-p ₀₀ (t))/t can tend to +t8 arbitrarily slowly.     

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