Geometric Brownian Motion
stochastic-process · 37 views
stochastic-processstochastic
What It Is
Geometric Brownian motion --- multiplicative random walk (dS/S = μdt + σdW), the basis of Black-Scholes option pricing. Log-normal distribution with positive skew
Interpretation
Standard analysis sees: long-range memory (persistent); nonstationary / drifting. The atlas additionally detects Nonstationarity:adf_pvalue.
What standard analysis sees
tail heaviness0.60
asymmetry0.21
occupancy0.66
short-range corr0.85
long-range memory0.89
spectral colour0.23
periodicity0.72
complexity0.67
time-irreversibility0.24
volatility clustering0.84
multifractality0.44
dimensionality0.24
nonstationarity0.88
What the atlas adds
Nonstationarity:adf_pvalue+3.2z
unit-root nonstationarity (ADF cannot reject random-walk null)
Atlas-extreme metrics the standard bank can’t predict for this source
Dodecagonal (Stampfli):pisot_triplet_coherence | +3.6z | bank-miss 1.4σ |
Composition
dtypefloat64
range[-3.241, 8.882]
unique values16384 / 16384
mean ± std2.77 ± 3.22
Render Gallery
Native > phase_plotraw
Native > timeseriesraw
Native > triple_latticeraw
Boltzmann > lag_map
Boltzmann > spin_grid
Cayley > default
Chladni > free_plate_nodal
Chladni > plate_bottom
Chladni > plate_top
_(centered)/signed_log_z/Geometric_Brownian_Motion.png)
Heisenberg (Nil) (centered) > signed_log_z
_(centered)/xy_path/Geometric_Brownian_Motion.png)
Heisenberg (Nil) (centered) > xy_path
Hodge–Laplacian > default
/barcode/Geometric_Brownian_Motion.png)
Inflation (Substitution) > barcode
/d_curve/Geometric_Brownian_Motion.png)
Inflation (Substitution) > d_curve
Information Theory > default
Julia Set > escape_histogram
Klein Bottle > default
Laplacian > default
Logarithmic Spiral > default
Möbius-S³ > mobius_cylinder
Möbius-S³ > s2_base_map
Ordinal Partition > default
/phi_spectrum/Geometric_Brownian_Motion.png)
Penrose (Quasicrystal) > phi_spectrum
Persistent Homology > barcode
Persistent Homology > h1_diagram
Predictability > default
Recurrence Quantification > default
Spectral Analysis > default
Spectral Graph > default
Spirograph > mode_spectrum
Spirograph > phasor_trajectory
Symplectic > flux_grid
Symplectic > phase_space
/default/Geometric_Brownian_Motion.png)
Ulam Spiral (Sacks) > default
/default/Geometric_Brownian_Motion.png)
Ulam Spiral (Square) > default
Visibility Graph > default
Wavelet Cascade > default
Atlas Position
| Nearest neighbor | Distance | |
|---|---|---|
| Brownian Walk | 2.29 | |
| Perlin Noise | 2.73 | |
| fBm (Persistent) | 2.97 |
Which Geometries Light Up
Catch24 › Catch24:CO_FirstMin_ac | rank 5/307 | 6096.6000 |
Catch24 › Catch24:SB_BinaryStats_mean_longstretch1 | rank 5/307 | 5348.1000 |
Dodecagonal (Stampfli) › Dodecagonal (Stampfli):pisot_triplet_coherence | rank 4/307 | 0.5245 |
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