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## THE FRACTIONAL MASTER EQUATION

I have shown that empirical waiting time distributions of volatility jumps follow Mittag-Leffler distributions for stocks and other assets. A random walk subordinated to such waiting times is a continuous-time random walk whose pdf follows the fractional master equation:
$\partial^{\beta}_t p(x,t) = -\lambda p(x,t) + \lambda \int_{-\infty}^\infty p(x-y,t) w(y) dy$

A solution to this equation is given by Saxena (2013):saxena-fractional-master-equation-2013.  This can be thought of as a time-changed version of a CTRW occurring with exponentially distributed waiting times: meerschaert-inverse-stable-subordinator-2011

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