Definition of Markov Transition Matrix

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A Markov transition matrix is a square matrix describing the probabilities of moving from one state to another in a dynamic system. In each row are the probabilities of moving from the state represented by that row, to the other states. Thus the rows of a Markov transition matrix each add to one. Sometimes such a matrix is denoted something like Q(x' | x) which can be understood this way: that Q is a matrix, x is the existing state, x' is a possible future state, and for any x and x' in the model, the probability of going to x' given that the existing state is x, are in Q.

Terms Related to Markov Transition Matrix

  • Markov Process
  • Markov Strategy
  • Markov's Inequality

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Moffatt, Mike. "Definition of Markov Transition Matrix." ThoughtCo, Mar. 28, 2017, thoughtco.com/markov-transition-matrix-definition-1148029. Moffatt, Mike. (2017, March 28). Definition of Markov Transition Matrix. Retrieved from https://www.thoughtco.com/markov-transition-matrix-definition-1148029 Moffatt, Mike. "Definition of Markov Transition Matrix." ThoughtCo. https://www.thoughtco.com/markov-transition-matrix-definition-1148029 (accessed January 17, 2018).