Finite State Markov Chains

Further notes

  • Step 1

    Select the number of states (1-8):

Step 2: enter the transition matrix

Enter the transition probabilities, where the entry in row i, column j is the probability of entering state j while in state i. All entries should be nonnegative and the sum of the entries in each row should be 1. If these conditions are not met, all negative entries are set to zero and the resulting rows of nonnegative entries are normalized to add to 1. If all entries in a row are 0, all transition probabilites are set to 1/(number of states).
From\To
Matrix you entered:
Transition matrix with adjustments (if any):
Equilibrium State Probabilities:

Ken Levasseur
Mathematical Sciences
UMass Lowell
Kenneth_Levasseur@uml.edu
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Notes on Mathematica

Notes

  1. The design of this page allows you to enter frequency data into the transiton matrix. For example, suppose that we are tracking 100 individuals that are in the states: (1) free, (2) in jail, and (3) on parol. Furthermore, assume that at some point in time there are 90, 5, and 5 individuals in these states. Finally assume that we know that after a certain amoung time, 85 of the 90 free individuals are still free, and 5 are in jail. We would enter 85, 5 and 0 into the first row of the matrix. A second row of 0, 3, 2 would indicate that two of the jailed individuals would go on parol, while the other three were still in jail. Finally assume that of the five on parol, three stay on parol, one is free and the fifth is back in jail (row three: 1, 1, 3). Try this example and see that in the long run roughly 65 individuals will be free if the transition ratios stay constant.
  2. An state that is not exited when it is entered is called an "absorbing state."
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