Abstract We propose a spatiotemporal point process model that enhances the classical Epidemic-Type Aftershock Sequence (ETAS) model. This is achieved with introduction of renewal main-shock arrival and we call this extension ETAS (RETAS) modification similar in spirit to Hawkes (RHawkes) but conditional intensity supports spatial component. It empowers reset upon main-shocks. allows for heavier...

For the stochastic present value of aggregate claims in the renewal risk model, a numerical algorithm is constructed based on the Monte Carlo and random process principle. The basic idea and design process of this algorithm is detailed. The numerical simulation results show that it is consistence with the theory analysis result under different parameter different distribution. The numerical alg...

Consider a renewal process {X,, n 2 1} for which there is defined an associated sequence of independent and identically distributed random variables {Bn, n 2 1 } such that Bn is the length of a subinterval of Xn. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process genera...

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the quenched LDP, i.e., we c...

This paper addresses sources contributing to the differences in the degree of recovery from extinction observed with different renewal paradigms. In two lick suppression experiments with rats, we assessed the role of the associative status of the acquisition context in both the weakness of AAC renewal and the sometimes observed weaker renewal resulting from an ABC design relative to an ABA desi...