The paper considers the superposition of modified Omori functions as a conditional intensity function for a point process model used in the exploratory analysis of earthquake clusters. For the examples discussed, the maximum likelihood estimates converge well starting from appropriate initial values even though the number of parameters estimated can be large (though never larger than the number of observations). Three datasets are subjected to different analyses, showing the use of the model to discover and study individual clustering features.

This paper uses the epidemic-type aftershock sequence (ETAS) point process model to study certain seismicity features of the Jiashi swarm of certain earthquakes, investigating in particular whether there is relative quiescence prior to the quite big events within the Jiashi sequence. The seven earthquake sequences studied occurred in the region of Jiashi, south of Tianshan Mountain, Xinjiang, China. The particular ETAS model that is developed is consistent with the reality of seismic activity. The various features of Jiashi swarm activity can be described as focusing in different stages. There is obvious precursory quiescence prior to most big events with Ms ≥ 6.0 within the Jiashi swarm. Thus, checking for relative quiescence can be use for earthquake prediction.

The annual earthquake predictions of the China Seismological Bureau (CSB) are evaluated by means of an R score (an R score is approximately 0 for completely random guesses, and approximately 1 for completely successful predictions). The average R score of the annual predictions in China in the period 1990–1998 is about 0.184, significantly larger than 0.0. However, background seismicity is higher in seismically active regions. If a ‘random guess' prediction is chosen to be proportional to the background seismicity, the expected R score is 0.123, and the nine-year mean R score of 0.184 as observed is only marginally higher than this background value. Monte Carlo tests indicate that the probability of attaining an R score of actual prediction by background seismicity based on random guess is about . It is concluded that earthquake prediction in China is still in a very preliminary stage, barely above a pure chance level.

A point process procedure can be used to study reservoir-induced seismicity (RIS), in which the intensity function representing earthquake hazard is a combination of three terms: a constant background term, an ETAS (epidemic-type aftershock sequence) term for aftershocks, and a time function derived from observation of water levels of a reservoir. This paper presents the results of such a study of the seismicity in the vicinity of the Tarbela reservoir in Pakistan. Making allowance for changes in detection capability and the background seismicity related to tectonic activity, earthquakes of magnitude ≥ 2.0, occurring between May 1978 and January 1982 and whose epicentres were within 100 km of the reservoir, were used in this analysis. Several different intensities were compared via their Akaike information criterion (AIC) values relative to those of a Poisson process. The results demonstrate that the seismicity within 20 km of the reservoir correlates with water levels of the reservoir, namely, active periods occur about 250 days after the appearance of low water levels. This suggests that unloading the reservoir activates the seismicity beneath it. Seasonal variations of the seismicity in an area up to 100 km from the reservoir were also found, but these could not be adequately interpreted by an appropriate RIS mechanism.

The thinking behind the original Black-Scholes formula is criticised on the grounds that it holds out the quite unrealistic prospect of risk-free operation, that it can sacrifice asset maximisation to exact meeting of the contract, and that it restricts investment to those stocks on which an option is being sold. An alternative approach is given, based on a model of risk-averse asset maximisation, which, while meeting these criticisms, gives the option price in the familiar form of a discounted and weighted conditional expectation of the seller's liability at maturity. This evaluation is extended to a completely general stochastic model of stock price evolution; consideration is also given to the possibility of seller's ruin.

The dynamics of host-macroparasite infections pose considerable challenges for stochastic modelling because of the need to take into account a large number of relevant factors and many nonlinear interactions between them. This paper focuses attention on the infection transmission process and the effects of specific modelling assumptions about the mechanisms involved. Some dramatically simplified linear models are considered; they are based on multidimensional linear birth and death processes, and are designed to illuminate qualitative effects of interest. Both single and compound infections are allowed. It is shown that such simple models can generate and increase dispersion of parasite counts, even among homogeneous hosts.

The paper studies a single-server two-queue priority system with changeover times and switching threshold. The server serves queue 1 exhaustively and does not remain at an empty queue if the other one is non-empty. It immediately switches from queue 2 to queue 1 when the length of the latter reaches some level M. Whenever service is changed from one queue to the other a changeover time is required. Arrivals are Poisson, service times and changeover times are independent and exponentially distributed. Using an analytic method we obtain the steady-state joint probability generating function of the lengths of the two queues. By means of this probability generating function some performance measures of the system such as mean length of queue and mean delay can be calculated.

The advantages and limitations of frequency domain and time domain methods for estimating the interannual variability arising from day-to-day weather events are summarized. A modification of the time domain method is developed and its application in examining a precondition for the frequency domain method is demonstrated. A combined estimation procedure is proposed: it takes advantage of the strengths of both methods. The estimation procedures are tested with sets of synthetic data and are applied to long time series of three meteorological parameters. The impacts of the different methods on tests of potential long-range predictability for seasonal means are also discussed.