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ABSORBING MARKOV EXPECTED TIME

Absorbing Markov Expected Time Calculator

Calculate expected steps to leave two transient states for an implicit absorbing state.

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Calculation steps

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    How to calculate

    Treat each transient-row probability deficit as a transition to one absorbing state.

    Expected steps t=(I−Q)⁻¹1; fundamental matrix N=(I−Q)⁻¹

    Worked example

    Q diagonal0.5 with no cross transitions gives mean absorption time2 steps from either state.

    Assumptions and input details

    Nonnegative substochastic2×2 block with finite absorption times. This includes the final transition into absorption as one step and does not include a waiting-time duration per step.

    Using this calculator

    Can I enter my own problem?

    Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.

    Are the results exact?

    Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.

    Is my input uploaded?

    The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.

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