# Create a discrete Markov chain process¶

This example details first how to create and manipulate a discrete Markov chain.

A discrete Markov chain , where is a process where discretized on the time grid such that: The transition matrix of the process can be defined such that: The library proposes to model it through the object DiscreteMarkovChain defined thanks to the origin (which can be either deterministic or uncertain), the transition matrix and the time grid.

from __future__ import print_function
import openturns as ot
import openturns.viewer as viewer
from matplotlib import pylab as plt
ot.Log.Show(ot.Log.NONE)


Define the origin

origin = ot.Dirac(0.0)


Define the transition matrix

transition = ot.SquareMatrix([[0.1, 0.3, 0.6], [0.7, 0.1, 0.2], [0.5, 0.3, 0.2]])


Define an 1-d mesh

tgrid = ot.RegularGrid(0.0, 1.0, 50)


Markov chain definition and realization

process = ot.DiscreteMarkovChain(origin, transition, tgrid)
real = process.getRealization()
graph = real.drawMarginal(0)
graph.setTitle('Discrete Markov chain')
view = viewer.View(graph) Get several realizations

process.setTimeGrid(ot.RegularGrid(0.0,1.0,20))
reals = process.getSample(3)
graph = reals.drawMarginal(0)
graph.setTitle('Discrete Markov chain, 3 realizations')
view = viewer.View(graph) Markov chain future 10 steps

future = process.getFuture(10)
graph = future.drawMarginal(0)
graph.setTitle('Markov chain future 10 steps')
view = viewer.View(graph) Markov chain 3 different futures

futures = process.getFuture(10,3)
graph = futures.drawMarginal(0)
graph.setTitle('Three Markov chain futures, 10 steps')
view = viewer.View(graph)
plt.show() Total running time of the script: ( 0 minutes 0.312 seconds)

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