Finite Markov Transition Calculator

How to use Finite Markov Transition Calculator

A row distribution advances by p(k)=p(0)P^k. Repeated squaring and compensated dot products bound work for large step counts. Probability conservation is checked without repairing invalid inputs or claiming convergence.

1. Enter json row-stochastic transition matrix, initial state probability fractions, transition steps.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• 2–20states,0–100000steps. Nonnegative probabilities with row/vector sums1 within8machine-epsilon×state-count. Derived mass error above1e-8 or detected underflow rejects. No stationary-distribution or forecast guarantee.
• Runs locally. Text/JSON fields are capped at30,000 characters; stricter page-specific and numeric-string limits also apply. Numeric inputs are bounded to magnitude1e15 and nonzero magnitude at least1e-100 unless an exact-string mode states otherwise. Approximate summaries use12 significant digits; CSV numeric cells retain the complete stored value and potentially formula-like string cells gain a protective apostrophe; unsupported, non-finite or detected underflow states return an error.