This article is concerned with objective estimation of the spatial intensity function of the background earthquake occurrences from an earthquake catalog that includes numerous clustered events in… Expand

[1] On the basis of the epidemic-type aftershock sequence (ETAS) model and the thinning procedure, this paper gives the method about how to classify the earthquakes in a given catalogue into… Expand

This paper contains an attempt to develop for discrete semigroups of infinite order matrices with nonnegative elements a simple theory analogous to the Perron-Frobenius theory of finite matrices. It… Expand

Summary Distributions appropriate to the description of long-term behaviour within an irreducible class of discrete-time denumerably infinite Markov chains are considered. The first four sections are… Expand

A method is developed for expanding arbitrary powers of the characteristic polynomial of a matrix. The coefficients are expressed in terms of matrix functions generalizing those of the permanent and… Expand

Suppose a forecasting scheme associates a probability p* with some observed outcome. The entropy score given to this forecast is then −logp*. This article provides a review of the background to this… Expand