M. Vidyasagar
- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0004
- Subject:
- Mathematics, Probability / Statistics
This chapter deals with Markov processes. It first defines the “Markov property” and shows that all the relevant information about a Markov process assuming values in a finite set of cardinality n ...
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This chapter deals with Markov processes. It first defines the “Markov property” and shows that all the relevant information about a Markov process assuming values in a finite set of cardinality n can be captured by a nonnegative n x n matrix known as the state transition matrix, and an n-dimensional probability distribution of the initial state. It then invokes the results of the previous chapter on nonnegative matrices to analyze the temporal evolution of Markov processes. It also estimates the state transition matrix and considers the dynamics of stationary Markov chains, recurrent and transient states, hitting probability and mean hitting times, and the ergodicity of Markov chains.Less
This chapter deals with Markov processes. It first defines the “Markov property” and shows that all the relevant information about a Markov process assuming values in a finite set of cardinality n can be captured by a nonnegative n x n matrix known as the state transition matrix, and an n-dimensional probability distribution of the initial state. It then invokes the results of the previous chapter on nonnegative matrices to analyze the temporal evolution of Markov processes. It also estimates the state transition matrix and considers the dynamics of stationary Markov chains, recurrent and transient states, hitting probability and mean hitting times, and the ergodicity of Markov chains.
