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THE FEUTEX TOOLKIT

Two-State Markov Equilibrium

Calculate long-run state proportions and persistence for a two-state transition process.

Probability workspace● Runs in your browser
01 Your input
02 Your result
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FormulaStationary A = b/(a+b); Stationary B = a/(a+b); Mean Run A = 1/a; Second Eigenvalue = 1-a-b
Sources and model references

Made for real tasks

  • Calculate long-run state proportions and persistence for a two-state transition process.
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Worked example

Inputs

Probability A to B
0.2 probability
Probability B to A
0.3 probability

Expected results

Stationary A
0.6 probability
Stationary B
0.4 probability
Mean Run A
5 steps
Second Eigenvalue
0.5 number

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter probability a to b, probability b to a.
  2. Use the displayed units and confirm the model assumptions.
  3. Calculate and compare the outputs against your input scenario.

Try this example

{
  "a": 0.2,
  "b": 0.3
}

Accuracy and scope

Homogeneous two-state Markov chain. When both transition probabilities equal one, the chain is periodic and does not converge from every initial state.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.