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BUILT-IN MATHEMATICA SYMBOL
DiscreteMarkovProcess
DiscreteMarkovProcess[i0, m]
represents a discrete-time, finite-state Markov process with transition matrix m and initial state 
.
DiscreteMarkovProcess[p0, m]
represents a Markov process with initial state probability vector 
.
DiscreteMarkovProcess[..., g]
represents a Markov process with transition matrix from the graph g.
Details
- DiscreteMarkovProcess is also known as a discrete-time Markov chain.
- DiscreteMarkovProcess is a discrete-time and discrete-state random process.
- The states of DiscreteMarkovProcess are integers between 1 and
, where 
is the length of transition matrix m. - The transition matrix m specifies conditional transition probabilities m
i, j
=Probability[x[k+1]=j
x[k]=i], where 
is the state of the process at time k. » - A discrete Markov process can be seen as a random walk on a graph, where the probability of transitioning from state
to state 
is specified by 
. - The transition matrix in the case of a graph g is constructed to give equal probability of transitioning to each incident vertex.
- DiscreteMarkovProcess allows m to be an
×
matrix with non-negative elements and rows that sum to 1, 
is an integer between 1 and 
, and 
is a vector of length 
of non-negative elements that sum to 1. - DiscreteMarkovProcess can be used with such functions as MarkovProcessProperties, PDF, Probability, and RandomFunction.
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