By Dauxois J.-Y., Druihlet P., Pommeret D.

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The distance from the point to the righthand end of the line is 7T1 (n); the distance to the left-hand end of the line is 7T2 (n). Then the end numbered 1 represents the vector [1 O], the initial state probability vector if the system starts in state 1 ; the point numbered 2 represents the vector [O l], corresponding to a system starting in state 2. We call such a diagram a state probability diagram. 2 shows the result. Suppose the customer was initially in state 1, n(O) = [I O]. 2]. 1 A geometric interpretation of a two-state process.

As the multinomial process whose transition probability matrix has as its common row the limiting state probability vector of the Markov process. The multinomial projection of a Markov process is a useful baseline for determining the importance of any computation of the dependencies introduced by the Markov process. The doubly stochastic process A doubly stochastic process is a Markov process whose transition probability matrix has the property that both rows and columns sum to one. Thus, it is not only true as usual that N ~Pit= 1 i = 1, 2, ...

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