Tag
Stochastic Processes
My approach to stochastic modeling is grounded in non-stationary SDE theory: the view that financial price dynamics are better described by a changing diffusion manifold than by a fixed parametric model. The Polybius engine models price dynamics as probability mass flow under a modified Fokker-Planck operator, using a Nyström diffusion map to track the evolving market manifold and random matrix theory to classify execution regimes in real time.
Blog
March 17, 2026
Price as Geometry: Resolution, Coarse-Graining, and the Structure of Market Noise
A rigorous tour through stationary and non-stationary models of price evolution, with geometric analysis at the forefront. From the random walk null and Black-Scholes as flat geometry, through mean reversion as curved Riemannian diffusion, wavelets, geometric harmonics, and information geometry, anchored throughout by empirical evidence from BTC/ETH millisecond data.
March 10, 2026
Manifolds: The Language of Modern Geometry
A rigorous construction of smooth manifolds from first principles: charts, tangent spaces, Riemannian metrics, curvature tensors, and geometric flows.
March 10, 2026
Kuramoto: How Order Emerges from Chaos
Fireflies, neurons, power grids: all governed by the same equation. A tour through the Kuramoto model, its order parameter, and the phase transition that turns noise into rhythm.