Together with co-authors Francesc Font-Clos, Gunnar Pruessner and Anna Deluca, Nicholas has studied the effect of thresholding on birth-death processes. The exact distribution of the duration time above threshold can be computed. The distribution is bi-power law with random walk exponent -3/2 initially, crossing over to birth-death exponent -2
asymptotically. These two regimes owe their existence to the multiplicative nature of the process, such that the threshold level sets a scale that separates two limiting behaviours. Crucially, the crossover between these two regimes scales with threshold level, such that for practical purposes the ultimate ‘true’ birth-death exponent
may never be observed. This may have implications for real-world data in the interpretation of threshold-specific decay exponents.
The article is published in New Journal of Physics: