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Markov Chain — Steady State

Find stationary distribution of a transition matrix.

Transition matrix P (rows sum to 1)
Result

Enter transition matrix.

Technical Description & Theory

What is Markov Chains Calculator and Why it Matters?

Markov chains model memoryless processes. The stationary distribution describes long-run behavior used in PageRank and queueing.

Mathematical Formula and Theory

Solve πP=π together with Σπᵢ=1 for the unique steady-state vector of an irreducible aperiodic chain.

How to Use This Calculator - Step by Step

  • Enter the row-stochastic transition matrix.
  • Click Find Steady State.

Solved Example with Full Calculation

P=[[0.9,0.1],[0.5,0.5]] yields π≈[0.833,0.167].