Definition of Markov Process: A Markov process is a stochastic process where all the values are drawn from a discrete set. In a first-order Markov process only the most recent draw affects the distribution of the next one; all such processes can be represented by a Markov transition density matrix. That is,

Pr{x_t+1 is in A | x_t, x_t-1,...} = Pr{x_t+1 is in A | x_t}

Example 1: x_t+1 = a + bx_t + e_t is a Markov process

For a=0, b=1 it is a martingale.

A Markov process can be periodic only if it is of higher than first order. (Econterms)

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