Abstract
The transition probability matrix is a matrix which contains some probability among two state. It has properties that every probability is non-negative and sum by row at every state is one. This paper want to determine the transition probability matrix by Laplace transform and exponential of a matrix methods. To construct the transition probability matrix by Laplace transform depends on identity matrix and generator matrix, but by matrix exponential method depends on generator matrix only. In this research obtained result that matrix exponential method easier than Laplace transformation. Because it is aided by software and programming. The transition probability matrix can be used to predict probability each other state. It could be used to predict value of state probability on long-term or limiting behavior, too. Otherwise, the transition probability mtrix could be used to construct occupancy times matrix. Keywords: Generator matrix, Laplace transform, Exponential matrix, Occupancy times matrix.
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