[rk-mlu]

First legacy port of milestone M1, stacked on #12 (base m1-end-to-end-slice; GitHub retargets it to main once #12 is merged). It satisfies the milestone gate "at least one legacy script is ported onto the new features".

What is added

File	Content
tests/regression/data/legacy_gbm_em_l2error.npz	Errors of the unmodified legacy function num_exp_GBM.compute_L2_errors, Euler–Maruyama only, with seed, parameters, NumPy version and SHA-256 checksums of num_exp_GBM.py, StochODEs.py, SODESolvers.py
tests/regression/data/README.md	Provenance and the code to regenerate the data
tests/regression/test_legacy_gbm.py	Rebuilds the legacy Brownian paths, wraps them as BrownianPath, and requires the library to reproduce the legacy errors
examples/strong_error_gbm.py	The experiment ported to the library API: errors, EOCs and 95 % confidence intervals; optional plot
tests/unit/test_examples.py	Smoke test of the example with small parameters

Reference data

The legacy script draws all step sizes from one generator default_rng(20250718), increments of shape (n_paths, m, n). These are other random numbers than WienerProcess.sample_path draws for the same seed, so the test rebuilds the legacy paths (the convention is documented in the test module). The legacy L2_error() is exactly the library's default strong error, uniformly on the grid with p = 2.

To keep the test fast, the data use 2000 paths and N = 10·2^k for k = 0, …, 5 instead of 50 000 paths and k ≤ 7. On the generating machine the library reproduces all six errors bitwise; the test uses rtol = 1e-12 because exp may round differently on other platforms.

Example vs. legacy at full size (50 000 paths)

N	legacy (new paths per N)	example (one coarsened path)	example 95 % CI
10	0.5646	0.5382	[0.4991, 0.5747]
20	0.4215	0.3966	[0.3814, 0.4112]
40	0.3069	0.3046	[0.2926, 0.3161]
80	0.2295	0.2219	[0.2161, 0.2276]
160	0.1658	0.1649	[0.1593, 0.1703]
320	0.1156	0.1164	[0.1135, 0.1193]
640	0.0847	0.0837	[0.0813, 0.0860]
1280	0.0592	0.0599	[0.0584, 0.0613]

Two independent Monte Carlo estimates; the differences are within their combined error (at N = 20 and 80 slightly outside the interval of the single estimate, as expected when comparing two estimates with heavy-tailed pathwise errors). The example needs about 3 GB with the book's parameters; --n-paths reduces that.

Not ported here

StrConvGBM.py (Python 2, unseeded) is superseded by num_exp_GBM.py. The Milstein part of num_exp_GBM.py and GBM_Milstein_L2error.py follow in M2; GBM_STM_* and GBM_BDF2_* with the implicit schemes in phase 2.

Checks

Fast suite 309 passed with PyTorch, 296 without; coverage 100 %; Ruff, mypy, codespell and Sphinx -W pass.

---

Generated by Claude Code