Abstract
summaryA class of piece‐wise linear stochastic processes is described, which can be used to model the gradual accumulation and sudden release of stress in earthquake models. Interest centres on the variance properties of the sequence of time points at which the sudden release (earthquakes) occur. Some general conditions are derived for the existence of moments, and under these conditions the variance properties are examined. It is shown that the point process of such events can have a bounded variance function, as is known to happen in the case of constant stress releases, only in this degenerate case. In the final section an example is examined which is closely related to the classical collective risk model.
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