Semi-Markov and Markov Chains
Markovian processes (semi-Markov and Markov) are processes included in a wider class of processes where one has an explicit time dependence (the dynamic aspect) as well as the stochastic character of the states evolution (therefore probabilistic). They are part of dynamic probabilistic systems. In practical situations the importance of this type of process is very great. Dynamic probabilistic systems are characterized by states, holding times in any given state and transitions among states. The present work deals almost exclusively with this important case of dynamic probabilistic systems. A physical, biological, technological economic system can be described by values of some variables considered as fundamental by those who observe a specified system. According to Howard, the state of a system “represents all we need to know to describe the system at any instant” . The systems under consideration do change in time and in an indetermininistic way -therefore, probabilistic. In this work we shall consider that the systems can occupy a finite number of states. A change in the system’s state is described by the waiting time and the transitions among the different states.
KeywordsMarkov Chain Markov Process Probability Transition Matrix Pattern Recognition System Pert Network
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