On the basis of a multidisciplinary approach we have unraveled the palaeo-earthquake history of a trenched section across the Peel Boundary Fault. The area shows at present one of the largest contrasts in relative motion on both sides of the fault on the basis of repeated levelling. The geological record for the last 25 thousand years, recovered in the trench, shows evidence of two heavy earthquakes (moment magnitude between 6.0 and 6.6), that occurred in a relatively short timespan around 15 thousands years ago. A third less severe event occurred somewhere in the mid Holocene. The time interval between the two large events is in the order of 1500 years, an interval comparable to that between the last volcanic explosions in the nearby Eifel area. Both records together seem to suggest a relation between large-scale faulting and volcanic activity in the nearby Eifel area, but this interpretation is based on one trench only and should be tested by opening more trenches in the zone that is assumed to be affected by these large events.

A simple model for a randomly oscillating variable is suggested, which is a variant of the two-state random velocity model. As in the latter model, the variable keeps rising or falling with constant velocity for some time before randomly reversing its direction. In contrast however, its propensity to reverse depends on its current value and it is for this desirable feature that the model is proposed here. This feature has two implications: (a) neither the changing variable nor its velocity is Markovian, although the joint process is, and (b) the linear differential equations arising in the case of our model do not have constant coefficients. The results given in this paper are meant to illustrate the straightforward nature of some of the calculations involved and to highlight the relationship with one-dimensional diffusions.

An unsolved problem in the design of a repetitive screening trial is the determination of a procedure which yields the optimal number of screens for efficient evaluation. An approach to this problem described in this paper is to use lead time properties of cases detected at screening to define a stopping rule. Previous results are generalized by allowing the intervals between screens to be arbitrary, and the probability of detecting preclinical disease to vary among screens.