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 ∙

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

Finally

12,666

9, 334

-0, 053

For β₂ = 0,99 we obtain

and the result

νι,∞ (0, 99) = 100 ∙ 5,5 + 0, 502 ∙ 2,5 + 1, 980 ∙ 0 = 550 + 1, 255 + 0 = 551, 255,
ν2,∞ (0, 99) = 100 ∙ 5, 5 - 0, 502 ∙ 2, 5 + 0 = 548, 745,
V3 ∞ (0, 99) = 550 + 0, 502 ∙ ⁵ + 1, 980 ∙ ²⁸ = 531,938.

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Finally

551, 255

548, 745

531, 938

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