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



V3,∞ (0,5) = 11 + 0, 666 5 + 1, 333

6

28

3


= 11 + 1, 388 - 12,441 = -0, 053.

Finally

12,666

'   (0, 5) =


9, 334

-0, 053

For β2 = 0,99 we obtain

'   (0, 99) =


1

1 - 0, 99


5, 5

5, 5

5, 5


ι 1

+ 1 + 0, 99

2, 5

1

2, 5

+ ---------

,
5

1 - 0, 5 0,99


28

3 -


6 J

5, 5

2, 5

0

= 100

5, 5

+ 0, 502

-2, 5

+ 1,980

0

5, 5

5

-          6 -

28

-—

L       3-1


and the result

νι,∞ (0, 99) = 100 5,5 + 0, 502 2,5 + 1, 980 0 = 550 + 1, 255 + 0 = 551, 255,
ν
2,∞ (0, 99) = 100 5, 5 - 0, 502 2, 5 + 0 = 548, 745,
V
3 ∞ (0, 99) = 550 + 0, 502 5 + 1, 980 28 = 531,938.

63

Finally

551, 255

'   (0,99) =


548, 745

531, 938

12



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