Here, 1,2 and 3 are the three possible states, and the arrows pointing from one state to the other states represents the transition probabilities pij. Pt(k)​=⎝⎜⎜⎜⎛​P(Xt+k​=1∣Xt​=1)P(Xt+k​=1∣Xt​=2)⋮P(Xt+k​=1∣Xt​=n)​P(Xt+k​=2∣Xt​=1)P(Xt+k​=2∣Xt​=2)⋮P(xt+k​=2∣Xt​=n)​……⋱…​P(Xt+k​=n∣Xt​=1)P(Xt+k​=n∣Xt​=2)⋮P(Xt+k​=n∣Xt​=n)​⎠⎟⎟⎟⎞​. In the hands of metereologists, ecologists, computer scientists, financial engineers and other people who need to model big phenomena, Markov chains can get to be quite large and powerful. Stationary distributions deal with the likelihood of a process being in a certain state at an unknown point of time. 333333333333%; padding:10px;
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Professional Certificate Program in Data Science for Business Decision Making