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N-stage transition probability
Consider the following, i.e., at time  the process is at state  , (say state number  ), while at time  , it is at state  , (say state number  ). Then the probability that from state number  to state number  is given by  , where
Pictorially we have the following diagram (Figure 1.16) to illustrate the one dimensional stochastic process.
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Figure 1.16: Illustration of concept of transition matrix |
Here the blue lines are  or  as the case may be, while the red line denotes,  , which can be expressed as one stage transition probability values as the case may be. Finally the green line denotes  , and in order to avoid confusion we consider the initial and final states as i and j ONLY.
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