关于NA列乘积和强收敛性的注记

讨论了NA随机变量序列乘积和的强收敛性,将王定成等(2002)关于NA列的广义Jam ison型加权和的几乎处处收敛性的结论推广到加权乘积和的强收敛性.     

随机过程序列部分和的收敛性的注记

讨论了随机过程序列部分和的弱收敛性，弱化了肖庆宪等人（1999）给出的条件并将结果推广到了混合序列的情形。     

Asymptotics of partial sums of linear processes with changing memory parameter*

We study the limit distribution of partial sums of nonstationary truncated linear process {X _t , t = 1,…, n} with long memory and changing memory parameter d _t,n ∈ (0,∞). Two classes of linear processes are investigated, namely, (i) the class of FARIMA-type truncated moving averages with time-varying fractional integration parameter and (ii) the class of time-varying fractionally integrated processes introduced in [A. Philippe, D. Surgailis, and M.-C. Viano, Invariance principle for a class of nonstationary processes with long memory, C. R. Acad. Sci., Paris, Sér. I, 342:269–274, 2006; A. Philippe, D. Surgailis, and M.-C. Viano, Time-varying fractionally integrated processes with nonstationary long memory, Theory Probab. Appl., 52:651–673, 2008]. The cases of fast-changing memory parameter (d _t,n = d _t does not depend on n) and slowly changing memory parameter (d _t,n = d(t/n) for some function d(τ), τ ∈ [0, 1]) are discussed. In the case of fast-changing memory, the limit partial sums process is a type II fractional Brownian motion (fBm) with the Hurst parameter equal to the global maximum of (d _t ) for class (i) processes and to the mean value of (d _t ) for class (ii) processes. In the case of slowly changing memory, the limit of partial sums for both classes (i) and (ii) is degenerate and “localized” at the global maximum of the memory function d(?); however, a nondegenerate limit of the partial sums process is shown to exist when time is suitably rescaled in the vicinity of the maximum point.     

A note on estimates for the growth order of sequences of multiple rectangular Fourier sums

We develop an optimal growth model of an open economy that uses both an old (“dirty” or “polluting”) technology and a new (“clean”) technology simultaneously. A planner of the economy expects the occurrence of a random shock that increases sharply abatement costs in the dirty sector. Assuming that the probability of an exogenous environmental shock is distributed according to the exponential law, we use Pontryagin’s maximum principle to find the optimal investment and consumption policies for the economy.     

Strong approximations for long memory sequences based partial sums,counting and their Vervaat processes

We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called Vervaat process. The first two of these processes are approximated by an appropriately constructed fractional Brownian motion, while the Vervaat process in turn is approximated by the square of the same fractional Brownian motion.     

A note on linear processes with tapered innovations

Lithuanian Mathematical Journal - In the paper, we consider the partial-sum process $$ {sum}_{k=1}^{left[ ntright]}{X}_k^{(n)}, $$ where $$ left{{X}_n^{(n)},kin mathbb{Z}right},nge 1, $$...     

A note on linear equations modeling birth-and-death processes

Cauchy's method of characteristics is applied to derive a comprehensive solution for a class of differential, partial differential and difference-differential equations encountered in the study of branching processes. The results are then used to address an unsolved Markov's generalized birth process.     

A note on character sums

Let $\text{S(k) = Σ}{}_{\mathrm{n=1}}{}^{\mathrm{p?1}}\text{(}\text{n}\text{p}\text{)n}{}^{\mathrm{k}}$ where p is a prime ≡ 3 mod 4 and k is an integer ≥ 3. Then S(k) frequently takes large values of each sign.     

A note on character sums

We investigate certain character sums and prove some discrepancy-type inequalities for incomplete sums.      

A short note on Dedekind sums

We will give a new proof for the fact that the values of Dedekind sums are dense on the real line.     

Ruin probability for correlated negative risk sums model with Erlang processes

This paper studies a Sparre Andersen negative risk sums model in which the distribution of ＂interclaim＂ time is that of a sum of n independent exponential random variables. Thus, the Erlang（n） model is a special case. On this basis the correlated negative risk sums process with the common Erlang process is considered. Integro-differential equations with boundary conditions for ψ（u） are given. For some special cases a closed-form expression for ψ（u） is derived.     

A general result on precise asymptotics for linear processes of positively associated sequences

Let {εt; t ∈ Z^＋} be a strictly stationary sequence of associated random variables with mean zeros, let 0〈Eε1^2〈∞ and σ^2=Eε1^2＋1∑j=2^∞ Eε1εj with 0〈σ^2〈∞.{aj;j∈Z^＋} is a sequence of real numbers satisfying ∑j=0^∞｜aj｜〈∞.Define a linear process Xt=∑j=0^∞ ajεt-j,t≥1,and Sn=∑t=1^n Xt,n≥1.Assume that E｜ε1｜^2＋δ′〈 for some δ′〉0 and μ（n）=O（n^-ρ） for some ρ〉0.This paper achieves a general law of precise asymptotics for {Sn}.     

Functional central limit theorems for self-normalized partial sums of linear processes

We prove an invariance principle under self-normalization by blocks for linear processes with summable filters and i.i.d. innovations in the domain of attraction of the normal distribution.     

A note on the cross-correlation function between two binary maximal length linear sequences

Let {a_j}and {a_dj} be two binary maximal length linear sequences of period 2ⁿ?1. The cross-correlation function is defined as for t = 0, 1,…, 2ⁿ ? 2. We find the values and the number of occurrences of each value of C_d(t) when $\text{d =}\text{2}{}^{\mathrm{<mtext>n</mtext><mtext>2</mtext>}}\text{?}\text{2}{}^{\mathrm{<mtext>n</mtext><mtext>4</mtext>}}\text{+}\text{1}\text{, n ≡}\text{0}$ (mod 8).     

A note on character sums in function fields

We give an improvement on a character sum estimate in ${\mathbb{F}}_q[t]$ and answer a question of Shparlinski.     

A normalizing system of natural deduction for intuitionistic linear logic

 The main result of this paper is a normalizing system of natural deduction for the full language of intuitionistic linear logic. No explicit weakening or contraction rules for -formulas are needed. By the systematic use of general elimination rules a correspondence between normal derivations and cut-free derivations in sequent calculus is obtained. Normalization and the subformula property for normal derivations follow through translation to sequent calculus and cut-elimination. Received: 10 October 2000 / Revised version: 26 July 2001 / Published online: 2 September 2002 Mathematics Subject Classification (2000): 03F52, 03F05 Keywords or phrases: Linear logic – Natural deduction – General elimination rules