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r-irber-irbe/proof-skills/skills/lean-math-stochastic/SKILL.md

lean-math-stochastic

Skill3 starsChanged 24 days agoApache-2.0View on GitHub

USE FOR: probability theory, stochastic processes, Markov chains, time-series analysis, ergodic theory. DO NOT USE FOR: deterministic dynamical systems (@lean-math-dynamical). TRIGGERS: probability, stochastic, Markov chain, time series, ergodic.

The file

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2 rules. About 0 are common, 0 are distinctive, and 2 are very specific to this project.

  • ≈0

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    This author's own choices. Worth a look.

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  1. Very specific:

    STOP if the proof needs a measurability instance not yet synthesised — handoff to @lean-math-foundations.

    line 45
  2. Very specific:

    STOP if the result you need is a deterministic dynamical-systems claim — re-route to @lean-math-dynamical.

    line 49

≈ “Common” is an estimate: at least 1 in 5 of the 350,495 skill files we read have a rule of the same kind, not the same words. “Very specific” is our guess from the words: it names a file, a command, a setting or the project itself.

Keep what fits and drop the rest. Your version, ready for your agents.
Files
SKILL.md

Lean 4 Stochastic Mathematics

Guide to formalizing probability, stochastic processes, and time series in Lean 4.

Routing

  • USE FOR: probability theory, stochastic processes, Markov chains, time-series analysis, ergodic theory, row-stochastic matrices, mixing times, spectral gaps, stationary distributions, and any stochastic dynamics in Lean 4.
  • DO NOT USE FOR: deterministic dynamical systems (delegate to @lean-math-dynamical); abstract measure-theoretic typeclass plumbing (delegate to @lean-math-foundations); pure topology (delegate to @lean-math-analysis); writing one specific proof (delegate to @lean-proof).

Workflow

  1. Identify the stochastic class (Part 1) — discrete-time chain, continuous-time process, martingale, stationary process, time-series model.
  2. Pick the matching Mathlib API (Probability.*, MeasureTheory.*) and apply the pattern below.
  3. Handoff to @lean-proof; if a measurability-instance gap blocks the proof, handoff to @lean-math-foundations; if a convergence step needs an analytic lemma, handoff to @lean-math-analysis.

Recovery & STOP

  • STOP if the proof needs a measurability instance not yet synthesised — handoff to @lean-math-foundations. (Recall IsFiniteMeasure.toSigmaFinite is a priority-100 instance — [SigmaFinite μ] is usually free given [IsFiniteMeasure μ].)
  • STOP if the result you need is a deterministic dynamical-systems claim — re-route to @lean-math-dynamical.

Handoffs

  • Predecessors: agent:gateway, skill:lean-proof (mid-proof probabilistic goal), skill:lean-research (ergodic / martingale API survey).
  • Successors: skill:lean-proof (apply the stochastic pattern), skill:lean-proof-review (audit the proof), skill:lean-math-foundations (measurability / SigmaFinite plumbing), skill:lean-math-analysis (convergence step).

Detailed reference

Full encyclopedic reference, decision trees, and lookup tables live in references/lean-math-stochastic-handbook.md .

See also

  • ../../references/lean-math-stochastic-handbook.md -- Complete lean-math-stochastic Handbook
  • ../lean-gateway/SKILL.md -- Top-level skill router

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