Activity Dependent Branching Ratios in Stocks, Solar X-ray Flux, and the Bak-Tang-Wiesenfeld Sandpile Model

Elliot Martin, Amer Shreim and Maya Paczuski

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Abstract: We define an activity dependent branching ratio that allows comparison of different time series $X_{t}$. The branching ratio $b_x$ is defined as $b_x= E[\xi_x/x]$. The random variable $\xi_x$ is the value of the next signal given that the previous one is equal to $x$, so $\xi_x=\{X_{t+1}|X_t=x\}$. If $b_x>1$, the process is on average supercritical when the signal is equal to $x$, while if $b_x

Date: 2009-10
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