{
  "parameters": {
    "lambda": 1.0,
    "D": 0.5,
    "baseline_variance": 0.5
  },
  "prediction_1_contraction": {
    "predicted_min_rate": 1.0,
    "observed_min_rate": 1.0000010680284839,
    "observed_fraction_below_lambda": 0.0,
    "rate_at_equal_radius_1": 2.5,
    "predicted_rate_at_equal_radius_1": 2.5
  },
  "prediction_2_small_beta_slope": {
    "prediction": "relative variance slope = -3D/lambda^2 + O(beta)",
    "predicted_relative_slope": -1.5,
    "observed_relative_slope": -1.470531280675109,
    "relative_error": 0.01964581288326069,
    "betas": [
      0.0,
      0.0001,
      0.0005,
      0.001,
      0.002,
      0.005
    ],
    "exact_variances": [
      0.5,
      0.49992502998145266,
      0.49962574768920137,
      0.4992529815889521,
      0.4985118538990524,
      0.49632277069557595
    ]
  },
  "prediction_3_monotonic_variance": {
    "prediction": "variance strictly decreases as beta increases",
    "betas": [
      0.0,
      0.02,
      0.05,
      0.1,
      0.2,
      0.5,
      1.0
    ],
    "exact_variances": [
      0.5,
      0.4860719266629153,
      0.4683252835020802,
      0.44435271185365816,
      0.4087807019337469,
      0.34512949814691035,
      0.28960238631924007
    ],
    "strictly_decreasing": true,
    "relative_gap_at_beta_0.5": 0.3097410037061793
  },
  "matched_euler_maruyama": {
    "linear_beta_0": [
      0.5045291340885324,
      0.00045780418770826123
    ],
    "cubic_beta_0.5": [
      0.34651163213824504,
      0.0002482549727557484
    ],
    "simulated_relative_gap": 0.3131979726716023,
    "dt": 0.005,
    "burn_steps": 3000,
    "sample_steps": 7000,
    "n_parallel": 4000
  }
}