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## Graph Laplacian component of volatility process

We had considered the market graph $G=(V,E)$ from daily closing prices of 1900 stocks, and we had looked at two components, from the first and fifth eigenvalues and they have an extremely complex noise.

We planned to do these steps with more care in a later phase of our volatility modeling project with the explicit purpose of understanding how to manage volatility storms globally.  But now we should look at denoising these with the Besov signal recovery by wavelet thresholding introduced by David Donoho.

Our general plan is to shoot for showing somehow that the Navier-Stokes type PDE on a graph can explain a major component of the volatility process on a graph.  These, recall, are just differential delay equations on $n$ variables of the form

$dx_i/dt = X(x_1,\dots,x_n)$

and the moment we have an invariant measure we can follow Poincare’s logic in his breakthrough recurrence theorem for Hamiltonian dynamics of many particles.

The links above have all the ideas that we need to proceed.