Create a four-state Markov chain from a randomly generated transition matrix containing eight infeasible transitions.

rng('default'); % For reproducibility 
mc = mcmix(4,'Zeros',8);

mc is a dtmc object.

Plot a digraph of the Markov chain.

figure;
graphplot(mc);

State 4 is an absorbing state.

Compute the state redistributions at each step for 10 discrete time steps. Assume an initial uniform distribution over the states.

X = redistribute(mc,10)

X = 11×4

    0.2500    0.2500    0.2500    0.2500
    0.0869    0.2577    0.3088    0.3467
    0.1073    0.2990    0.1536    0.4402
    0.0533    0.2133    0.1844    0.5489
    0.0641    0.2010    0.1092    0.6257
    0.0379    0.1473    0.1162    0.6985
    0.0404    0.1316    0.0765    0.7515
    0.0266    0.0997    0.0746    0.7991
    0.0259    0.0864    0.0526    0.8351
    0.0183    0.0670    0.0484    0.8663
      ⋮

X is an 11-by-4 matrix. Rows correspond to time steps, and columns correspond to states.

Visualize the state redistribution.

figure;
distplot(mc,X)

After 10 transitions, the distribution appears to settle with a majority of the probability mass in state 4.

Consider this theoretical, right-stochastic transition matrix of a stochastic process.

Create the Markov chain that is characterized by the transition matrix P.

P = [ 0   0  1/2 1/4 1/4  0   0 ;
      0   0  1/3  0  2/3  0   0 ;
      0   0   0   0   0  1/3 2/3;
      0   0   0   0   0  1/2 1/2;
      0   0   0   0   0  3/4 1/4;
     1/2 1/2  0   0   0   0   0 ;
     1/4 3/4  0   0   0   0   0 ];
mc = dtmc(P);

Compute the state redistributions at each step for 20 discrete time steps.

X = redistribute(mc,20);

Animate the redistributions in a histogram. Specify a half-second frame rate.

figure;
distplot(mc,X,'Type','histogram','FrameRate',0.5);