The aim of this work is to quantitatively set up a simple hypothesis for oc
currence of earthquakes conditioned by prior events, on the basis of a prev
iously existing model and the use of recent instrumental observations. A si
mple procedure is presented in order to determine the conditional probabili
ty of pairs of events (foreshock-mainshock, mainshock-aftershock) with shor
t time and space separation. The first event of a pair should not be an aft
ershock, i.e., it must not be related to a stronger previous event. The Ita
lian earthquake catalog of the Istituto Nazionale di Geofisica (ING) (1975-
1995, M greater than or equal to 3.4), the earthquake catalog of the Japan
Meteorological Agency (JMA) (1983-1994, M greater than or equal to 3.0) and
that of the National Observatory of Athens (NOA) (1982-1994, M greater tha
n or equal to 3.8) were analyzed. The number of observed pairs depends on s
everal parameters: the size of the space-time quiescence volume defining no
naftershocks, the inter event time, the minimum magnitude of the two events
, and the spatial dimension of the alarm volume after the first event. The
Akaike information criterion has been adopted to assess the optimum set of
space-time parameters used in the definition of the pairs, assuming that th
e occurrence rate of subsequent events may be modeled by two Poisson proces
ses with different rates: the higher rate refers to the space-time volume d
efined by the alarms and the lower one simulates earthquakes that occur in
the nonalarm space-time volume. On the basis of the tests carried out on th
e seismic catalog of Italy, the occurrence rate of M greater than or equal
to 3.8 earthquakes followed by a M greater than or equal to 3.8 mainshock w
ithin 10 km and 10 days (validity) is 0.459. We have observed, for all thre
e catalogs, that the occurrence rate density lambda for the second event of
a couple (mainshock or aftershock) of magnitude M-2 subsequent to a nonaft
ershock of magnitude M-1 in the time range T can be modeled by the followin
g relationship: lambda (T, M-2) = 10(a)' (+ b(M1) (- M2)) with b varying fr
om 0.74 (Japan) to 1.09 (Greece). The decrease of the occurrence rate in ti
me for a mainshock after a foreshock or for large aftershocks after a mains
hock, for all three databases, obeys the Omori's law with p changing from 0
.94 (Italy) to 2.0 (Greece).