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

q=

After some easy transformation we receive:

T 1 - 0, 5β   -0, 4β

⁼    -0, 5β   1 - 0, 6β

and

1         1 - 0,6β    0,5β

det (I - βP)[   0, 4β    1 - 0, 5β

11     β²

-₁₀ β + β₀ = (i — β )(1 — 0, ιβ ).

Finally

Now as an example, we decompose into partial fractions the first element of ma-
trix (1 - βP)^-1.

We receive:

1 - 0,6β =  D1¹1  ₊    D21    =   4   ₊     5

^{(1 - β})^{(1 - 0,} 1^β)    ^{(1 - β})    ^{(1 - 0,} 1^β)    ^{(1 - e)    (1 - 0,} 1^β)

because

1 - 0, 6β = D₁¹₁ (1 - 0, 1β) + (1 - β) D₁²₁.

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