There is a long run expression of Markov process which is known as steady-state probabilities which shows thatwhen the sample of a Markov chain cannot be reduced further. It is shown by:

Lt pij(n) = ∏j (i.e., independent of i)

Where ∏j shows the steady state and is denoted by the equation:

In the above expression we see that ∏j is the steady state because in the process of finding a probability of a state say j, in the long run the transition slowly tends to return back to ∏j .

We also have an equation as:

µijstands for expected recurrence time. This shows the mean recurrence time of each state.

Steady-State Probabilities 1

Steady-State Probabilities 2

Steady-State Probabilities 3

Steady-State Probabilities 4

Steady-State Probabilities 5

Steady-State Probabilities 6

Steady-State Probabilities 7

Steady-State Probabilities 8

Steady-State Probabilities 9

 

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