Let be a filtered probability space with a discrete filtration (although the results we are going to discuss hold for continuous random processes as well). We say that a random process on possesses the Markov property if

for all . We see this often in the following form

or simply with with . This is the Markov property.

The following is just wrong: For a sequence of sets where

A very easy and straightforward way to verify that this is false is to set , that is, provide no information about and provide the information , i.e., $B_{k-1}=\{x\}$ which actually offers some information. Then, according to the wrong statement above, it would be

Although, it should naturally be . That is, the information that is completely expunged.

Reference: K.L. Chung, *Green, Brown and Probability, *World Scientific, 1995 [Chap. 5].

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