AN ANALYTICAL METHOD TO CALCULATE THE ERGODIC AND DIFFERENCE MATRICES OF THE DISCOUNTED MARKOV DECISION PROCESSES



and for the second state

ν2,∞ (0,5) = 2 1 - 1, 052 4 = -2, 208.

For β = 0, 99 we obtain

ν(0,99) = 100


-4


and

νι,∞ (0, 99) = 100 + 5 = 105,

ν2,∞ (0, 99) = 100 - 4 = 96.

Example 2

Let N = 3 and

0 1     0

9     8     3 ^

P =

1 0     0

, R =

3 -7 -2

0 0, 5 0, 5

5 -9   3

Hence

-8
-3

Further calculations give us the following results:

1 β 0

(I - βP ) =


-β 1       0

0 0,5β 1 - 0, 5β

10



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