nonlinear fractional diffusions with python code for calculating Green functions
July 18, 2015 by zulfahmed
Dear Professor Donoho,
Attached is a write-up that includes completed (still to be debugged/tested) code for Mittag-Leffler function and the formula for Green function on R^d for fractional diffusions, taking us one step further toward being able to simulate these for phase transition effects using generic nonlinear forcing term F. This last is crucial for flexibility. Our major hypothesis is that sample paths of nonlinear fractional diffusions are likely to be better candidates for fitting empirical continuous time univariate financial volatility series than the sample paths of diffusions which are the industry standard in finance as Samuelson school at MIT had established in the 1970s.
This is a major step in ensuring that we can consider quantitative sources for global financial volatility directly in continuous-time models rather than seek speculation-induced and groping-in-the-dark explanations based on ‘irrational exhuberance’ and behavioral ideas that go back essentially to Laplace’s Essays on Probability with very little intellectual novelty.