Task: Expand the Random Walk knowledge page

Table of Contents

This page documents a task in the Documentation improvements story. It captures the goal, current status, acceptance, and any notes or results.

1. Goal

The Random Walk page covers the definition, the Markov property and the Wiener-process limit. An external write-up on random walks passes through five themes, three of which the page does not carry: stationary increments against a non-stationary level, unit-root persistence, and first-passage questions. Add those three sections, tie each to the ORE Studio process it bears on, and attribute the source.

2. Status

Field Value
State DONE
Parent story Documentation improvements
Now Nothing.
Waiting on Nothing.
Next Nothing.
Last touched 2026-09-10

3. Acceptance

  • The page states that the increments are stationary while the level is not, with the variance growing with the horizon.
  • The page states the unit-root property and contrasts it with a mean-reverting process.
  • The page covers first-passage times and names an ORE Studio product family that asks the question.
  • Each new section links to the related knowledge pages by id.
  • The source is attributed in Further reading, with author, publication and retrieval date.
  • The site build publishes the page without error.

4. Plan

Fold the three missing themes into the existing page rather than creating a second page, because the page already exists and the new material is the same subject. Sit the new sections between the definition and the Markov section, so the page runs definition, stationarity, unit root, Markov property, continuous-time limit, first passage. Grade the page against the code review checklist; the class check for a doc-only change is the site build.

5. Notes

6. Test Scenarios

Manual QA scenarios (scaffolded via compass add test_scenario, run through the QA Validation Runner panel) that verify this task. Link new ones here as they're created; the scenario doc itself links back via its "Verifies task" field.

Scenario State Notes
     

7. PRs

PR Title
#2054 [doc] Expand the random walk knowledge page

8. Review

# Comment summary File Decision Notes
1 Citation used square brackets, which org renders as literal text and which read as a malformed link. doc/knowledge/domain/random_walk.org Accepted Quoted the post's opening line as the title, matching the Pearson and Donsker entries.
2 Attribution sits in Further reading, not in a top-level * Source block as in lightyear_pnl_approach.org. doc/knowledge/domain/random_walk.org Declined That convention is for pages that are about external material; here the post is one of five references.
3 #+description was not extended to mention first passage. doc/knowledge/domain/random_walk.org Declined Still accurate at the granularity that descriptions work at.
4 Bot review: line 152 runs to ~93 columns where the file wraps at ~72-76; move the Generic Barrier Option link to its own line. doc/knowledge/domain/random_walk.org Accepted Rewrapped, so the link now sits on its own line as the Geometric Brownian Motion link does.

9. Result

Added three sections to the Random Walk page — stationarity of the increments against the non-stationarity of the level, the unit root and its contrast with mean reversion, and first-passage times — plus the source in Further reading. Every new section links to the related knowledge pages by id. The site build publishes the page clean.

Emacs 29.3 (Org mode 9.6.15)