#Markov stationary distribution on a 5x5 matrix

19 messages · Page 1 of 1 (latest)

peak wedge
#

Hey there !

So what i have done is :

I made an inequation with :

1/3y + 2/3t = x
w = y
y = z
w = t
1/3+2/3z = w
x +y+z+w+t = 1

I found the result pi = [1/5, 1/5, 1/5, 1/5, 1/5]

Problem is when I do pi * P, I don't get pi again !

Is there a problem in my calculs?

Thanks a lot for reading

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jolly kelpBOT
#
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sinful kayak
#

does a stationary solution exist in the first place?

#

you want to solve x = xP

#

are you doing pi * P or P * pi

#

these are not the same

#

$$ \pi = \pi P \Leftrightarrow (E-P)\pi = 0 $$

loud mossBOT
sinful kayak
#

with the added condition that x+y+z+w+t = 1

sinful kayak
#

@peak wedge

peak wedge
#

Sorry I haven't seen!

peak wedge
peak wedge
#

something i struggle with if there is a solution then there is a limit? But my graph with the state is periodic (there is no self absorbing state so they keep moving)

peak wedge
#

+close

weary tartanBOT
# peak wedge +close
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weary tartanBOT
# weary tartan

Thank you for your feedback! aL has been awarded 1 helper_points. They now have 825 helper_points. They have 3 helper_points daily left for today.