A semi-Markov model estimating the waiting times and magnitudes of large earthquakes is proposed. The model defines a discrete-time, discrete-state process in which successive state occupancies are governed by the transition probabilities of the Markov process. The stay in any state is described by an integer-valued random variable that depends on the presently occupied state and the state to which the next transition is made. Basic parameters of the model are the transition probabilities for successive states, the holding time distribution, and the initial conditions (the magnitude of the most recent earthquake and the time elapsed since then).

The model was tested by examining compatibility with historical seismicity data for large earthquakes in the circum-Pacific belt. The examination showed reasonable agreement between the calculated and actual waiting times and earthquake magnitudes. The proposed procedure provides a more consistent model of the physical process of gradual accumulation of strain and its intermittent, nonuniform release through large earthquakes and can be applied in the evaluation of seismic risk.

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