Relationship between the asymptotic behavior of exponents of a multidimensional exponential series and the asymptotic behavior of its coefficients in a neighborhood of singular points

We study the relation of the asymptotic behavior of the coefficients of multidimensional exponential series to the asymptotic behavior of its sum by using theR-order of the growthp _QR (a ₁,...,a _n ) in an octantQ(a ₁,...,a _n ). Bryansk Pedagogical Institute, Bryansk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1193–1200, September, 1999.     

On the asymptotic behavior of the Laurent coefficients of a class of Dirichlet series

Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration admit a functional equation. The second author was supported by the FWF project S381O.     

The asymptotic behavior of a structured cell population

This paper deals with a mathematical model of an age-cycle structured proliferating cell population. Individual cells are distinguished by age and cell cycle length. We consider a general biological rule corresponding to a non-compact boundary condition. We give the asymptotic behavior of the generated semigroup in the uniform topology.     

Convex conservation laws with discontinuous coefficients. existence,uniqueness and asymptotic behavior

Existence and uniqueness is proved, in the class of functions satisfying a wave entropy condition, of weak solutions to a conservation law with a flux function that may depend discontinuously on the space variable. The large time limit is then studied, and explicit formulas for this limit is given in the case where the initial data as well as the x dependency of the flux vary periodically. Throughout the paper, front tracking is used as a method of analysis. A numerical example which illustrates the results and method of proof is also presented.     

Estimating function with asymptotic bias and its estimator

We introduce the estimating function with asymptotic bias and investigate the asymptotic behavior of the estimator based on it by using their relationship. The estimator based on the estimating function with asymptotic bias has the asymptotic normality with asymptotic bias. We show that this theory has several interesting applications in practical statistics.     

The growth on a positive ray of entire functions with real Taylor coefficients

It is proved that if the Taylor coefficients of an entire transcendental function change sign sufficiently infrequently, then such a function increases on a positive ray in the same way as in the whole plane.Translated from Matematicheskie Zametki, Vol. 14, No. 4, pp. 577–588, October, 1973.     

The asymptotic behavior of fragmentation processes

The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate their pathwise asymptotic behavior as t. In the so-called homogeneous case, we first point at a law of large numbers and a central limit theorem for (a modified version of) the empirical distribution of the fragments at time t. These results are reminiscent of those of Asmussen and Kaplan [3] and Biggins [12] for branching random walks. Next, in the same vein as Biggins [10], we also investigate some natural martingales, which open the way to an almost sure large deviation principle by an application of the Gärtner-Ellis theorem. Finally, some asymptotic results in the general self-similar case are derived by time-change from the previous ones. Properties of size-biased picked fragments provide key tools for the study. Mathematics Subject Classification (2000) 60J25, 60G09