Chun Su

Large deviations for heavy-tailed random sums in compound renewal model

In the present paper we investigate the precise large deviations for heavy-tailed random sums. First, we obtain a result which improves the relative result in Kluppelberg and Mikosch (J. Appl. Probab. 34 (1997) 293). Then we introduce a more realistic risk model than classical ones, named the compound renewal model, and establish the precise large deviations in this model.

Complete convergence for weighted sums of NA sequences

Under general weighting coefficient, we obtain the complete convergence for weighted sums of negatively associated (NA) sequences, and discuss its necessity. The results on i.i.d. setting of Chow [Ann. Math. Statist. 37 (1966) 1482-1492], Thrum [Probab. Theory Rel. Fields 75 (1987) 425-430] and Li et al. [J. Theor. Probab. 8 (1995) 49-76] are extended and generalized. Also, the sufficient part of Wang et al.s [Sci. in China 41 (1998) 939-949] Theorem 1 is extended.

Limit theorems for the number and sum of near-maxima for medium tails ☆

Let X1,X2,..., be a sequence of i.i.d. random variables. Xj, j[less-than-or-equals, slant]n is called a near-maximum iff Xj falls within a distance of the maximum Mn=max{X1,...,Xn}. In this paper, we focus on medium tailed distributions. A useful relationship on the number of near-maxima is built between general medium tailed and exponential distributions. Limit properties of the ratio Sn(a)/Sn are discussed, where Sn(a) is the sum of near-maxima.

Limiting behavior of uniform recursive trees

Abstract The authors consider the limiting behavior of various branches in a uniform recursive tree with size growing to infinity. The limiting distribution of ζ n,m , the number of branches with size m in a uniform recursive tree of order n, converges weakly to a Poisson distribution with parameter 1 m with convergence of all moments. The size of any large branch tends to infinity almost surely.