5d06f0ab57
docs: replace all ASCII/Unicode diagram blocks with matplotlib SVG figures
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Replace 23 ASCII/Unicode text diagram code-blocks in mathematical_foundations.md
with professionally rendered matplotlib SVG figures.
Changes:
- Add docs/source/_gen_diagrams.py: Python script generating all 23 SVG figures
with consistent styling (white bg, blue/orange/green/red palette, scipy/numpy/
matplotlib Agg backend)
- Add docs/source/_static/diagrams/*.svg: 23 rendered SVG figures covering:
§1 DE/random-walk/BM/GBM, §2 Ito/Picard/FP/EM/OU, §3 Poisson/Merton/Levy,
§6 Kalman, §7 MCMC, §9 KL/Fisher, §10 curvatures/natural-gradient
- Update mathematical_foundations.md: all ASCII art code-blocks replaced with
MyST {figure} directives pointing to the generated SVGs
- Sphinx build: clean success, all 23 SVGs copied to build, 1 pre-existing warning
Resolves: user request for professional publication-quality figures instead of
ASCII/Unicode art (which was too low-level for publication)
2026-03-07 11:29:14 +01:00
b41618c627
docs(theory): enrich Section 4 optimal control with 4 worked examples
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- Add HJB/PMP/HJBI comparison overview table
- Add Merton 1969 portfolio allocation example (log-utility, constant fraction)
- Add Almgren-Chriss inventory liquidation example (LQR + TWAP-like schedule)
- Add PMP costate derivation for Merton problem
- Add American option as viscosity example (variational inequality, smooth-pasting)
- Explain jump integral term intuition in HJBI
- Add shooting method pseudocode for PMP
- Mirror all enrichments in LaTeX .tex source
- Regenerate PDF (13 pages, cross-refs resolved)
2026-03-06 20:22:35 +01:00
48220de0ce
docs(theory): enrich mathematical foundations with 10 sections
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Sections added/expanded:
- DE: operator table, jDE self-adaptive rules, convergence theorem
- Stochastic Processes: 4-axiom BM, Ito calculus+lemma, SDE table, OU MLE
- Jump Processes: Poisson, Merton formula, Levy-Khintchine theorem+table, SDE generator
- Optimal Control: HJB boxed PDE, LQR Riccati, PMP costate theorem, HJBI jumps, viscosity solutions
- Mean Field Games: HJB+KFP system, fixed-point pseudocode, Lasry-Lions convergence
- Kalman Filtering: predict/update recursion, KL-minimization view, Kalman-Bucy Riccati
- MCMC: MH accept-reject, optimal step h~2.38/sqrt(d), MALA+Langevin SDE
- HMM: full Baum-Welch E/M (alpha/beta/gamma/xi), Viterbi max-product
- Information Theory: Shannon entropy, KL+Gibbs, Fisher info+Cramer-Rao, mRMR, natural gradient preview
- Differential Geometry: Riemannian manifold+geodesic+Christoffel, Fisher-Rao metric,
Amari natural gradient, dually-flat exp families, Lie groups, symplectic geometry+PMP, sectional curvature
- Quick Reference table (15 rows), 11 full references
- Sphinx build clean (1 unrelated chardet warning only)
2026-03-06 19:14:43 +01:00
ThotDjehuty