Why proportion of black balls in Polya Urn is not Markovian? How could i prove that the process followed by the proportion of black balls in a Polya urn model (with white and black balls) is not markovian?
Thank you in advance
 A: No.   It is Marcovian. (correction: see edit below)
A process is considered to be Marcovian if the future state can be predicted as well knowing its current state as it can knowing the full history.   That is, conditional only the present state of the system its future states are independent of its past states.
The Polya Urn system is sampling with double replacement.   (On each turn, sample a ball, then return it and a new ball of the same colour).   The future state of this system may be statistically determined solely by the current state (how many balls of each colour are currently within the urn), without regard to its history (i.e. in what order the balls had been drawn previously).   This satisfies the above property.

Edit:
Correction:   If the current state of the system is measured solely by the proportion of black to white balls, rather than their counts, then the future states are not independent of the history.   You do then require additional information to predict future status, since the degree change of proportions on each step is also dependent on amount of balls in the urn.   At least knowledge of one prior proportion would be required to obtain this.
While a Polya System of states measured by amounts is Marcovian, a Polya System of states measured only by proportions is not Marcovian.
