Let F (Z) = P r arZ r be a rational generating function in the d variables Z1, . . . , Zd. Asymptotic formulae for the coefficients ar may be obtained via Cauchy’s integral formula in Cd. Evaluation of this integral is not as straightforward as it is in the univariate case. This paper discusses geometric techniques that are needed for evaluation of these integrals and surveys classes of functio...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performa...

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions unde...

Within the Liapunov framework, a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed. Unlike with classical Liapunov theory, the time derivative of the V -function, taken along solutions of the system, may have positive and negative values. It is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogene...

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis techniques as it is usually done in this context. A new explicit representation of periodic functions involved is obtained at the same time.