The clock advance picture of the ETAS model

In this presentation we propose to extend the ETAS model to micro-seismic
events. For that we interpret the triggered events in an ETAS model as individual
local clock advances of an independent background process. The solution of the ETAS model thus
becomes the sum of an infinite Markov chain of independent time adjusted
background processses. This allows the incorporation of events at all scales. No artificial small
magnitude cutoff is needed. We also discuss the implication to the stability of the ETAS model without a large magnitude cutoff. We give a proof that the seismicity explodes in finite time as soon as the expected production rate becomes overcritical.