STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

Let {Xt,t ≥ 1} be a moving average process defined by Xt = ∑^∞ k=0 αkξt-k, where {αk,k ≥ 0} is a sequence of real numbers and {ξt,-∞ 〈 t 〈 ∞} is a doubly infinite sequence of strictly stationary dependent random variables. Under the conditions of {αk, k ≥ 0} which entail that {Xt, t ≥ 1} is either a long memory process or a linear process, the strong approximation of {Xt, t ≥ 1} to a Gaussian process is studied. Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.

The Strong Approximation of Functions by Fourier-Vilenkin Series in Uniform and H?lder Metrics

We will study the strong approximation by Fourier-Vilenkin series using matrices with some general monotone condition. The strong Vallee-Poussin, which means of Fourier-Vilenkin series are also investigated.

ON STRONG APPROXIMATION APPLIED TO POST-WIDDER OPERATORS

We introduce modified Post-Widder operators in polynomial weighted spaces of differentiable functions and we study strong approximation for them.

ON THE UNIFORM STRONG APPROXIMATION OF MARCINKIEWICZ TYPE FOR MULTIVARIABLE CONTINUOUS FUNCTIONS

The rate of uniform strong approzimation of Marcinkiewicz type for multivariable continuous functions is obtained in this paper as follows：‖1/k＋1 ^k∑j=0 ｜Sj（f）-f｜^q‖≤C/k＋1^k∑j=0 Ej^q（f）,where Sj（f） denotes the square partial Fourier sum off and Ej（f） denotes the square best approximation of f by trigonometric polynomials of degree（j,j,…,j）,j=0,1,2.…

On the Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline

For a 2-station and 3-class reentrant line under first-buffer first-served(FBFS)service discipline in light traffic,we firstly construct the strong approximations for performance measures including the queue length,workload,busy time and idle time processes.Based on the obtained strong approximations,we use a strong approximation method to find all the law of the iterated logarithms(LILs)for the above four performance measures,which are expressed as some functions of system parameters:means and variances of interarrival and service times,and characterize the fluctuations around their fluid approximations.

Strong Approximation by Riesz Means on Compact Symmetric Spaces

The rates of strong approximation by Riesz means on compact symmetric spaces are established.

Strong Approximations of Martingale Vectors and Their Applications in Markov-Chain Adaptive Designs

The strong approximations of a class of R^d-valued martingales are considered.The conditions usedin this paper are easier to check than those used in [3] and [9].As an application,the strong approximation ofa class of non-homogenous Markov chains is established,and the asymptotic properties are established for themulti-treatment Markov chain adaptive designs in clinical trials.

Strong Approximation Theorems for Sums of Random Variables when Extreme Terms are Excluded

Let{X_n:n≥1}be a sequence of i.i.d.random variables and let X_n^((r))=X_j if|X_j| is the r-th maximum of |X_1|……|X_n|.Let S_n=X_1+…+X_n and ^(r)S_n=S_n(X_n^(1)+…+X_n^(r)).Sufficient and necessary conditions for ^(r)S_n approximating to sums of independent normal random variables are obtained.Via approximation results,the convergence rates of the strong law of large numbers for ^(r)S_n are studied.

Strong Approximation Method and the(Functional)Law of Iterated Logarithm for GI/G/1 Queue

In this paper, a unified method based on the strong approximation(SA) of renewal process(RP) is developed for the law of the iterated logarithm(LIL) and the functional LIL(FLIL), which quantify the magnitude of the asymptotic rate of the increasing variability around the mean value of the RP in numerical and functional forms respectively. For the GI/G/1 queue, the method provides a complete analysis for both the LIL and the FLIL limits for four performance functions: The queue length, workload, busy time and idle time processes, covering three regimes divided by the traffic intensity.

A strong approximation of self-normalized sums

Let {X,Xn,n1} be a sequence of independent identically distributed random variables with EX=0 and assume that EX2I(|X|≤x) is slowly varying as x→∞,i.e.,X is in the domain of attraction of the normal law.In this paper a Strassen-type strong approximation is established for self-normalized sums of such random variables.

Strong approximation for ρ-mixing sequences

We establish strong invariance principles for sums of stationary p-mixing random variables with finite and infinite second moments under weaker mixing rates. Some earlier results are improved. As applications, some results of the law of the iterated logarithm with finite and infinite variance are obtained, also a conjecture raised by Shao in 1993 is solved

A Strong Approximation Theorem for Quasi-associated Sequences

By combining the Csorgo-Révész quantile transform methods and the Skorohod-Strassen martingale embedding theorem, we prove a strong approximation theorem for quasi-associated random variables with mean zero and finite （2 ＋ δ）th moment under polynomial decay rate. As a consequence, the decay rate for a strong approximation theorem of associated sequences of Yu （1996） is weakened.

Strong Approximations for a Kumar-Seidman Network under a Priority Service Discipline

In this paper,we derive the strong approximations for a four-class two station multi-class queuing network（Kumar-Seidman network） under a priority service discipline.Within a group,jobs are served in the order of arrival,that is,a first-in-first-out disciple,and among groups,jobs are served under a pre-emptiveresume priority disciple.We show that if the input data（i.e.,the arrival and service processe） satisfy an approximation（such as the functional law-of-iterated logarithm approximation or the strong approximation）,the output data（the departure processes） and the performance measures（such as the queue length,the work load and the sojourn time process） satisfy a similar approximation.

Strong Approximation for a Toric Variety

Let X be a toric variety over a number field k with k[X]×=k×.Let W■X be a closed subset of codimension at least 2.We prove that X\W satisfies strong approximation with algebraic Brauer-Manin obstruction.

Strong Approximation of Locally Square-Integrable Martingales

In this paper, we consider the strong approximation for locally square-integrable martingales. In our results, the limit process may be a process with jumps. This is an extension of the former results.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.

THE LAW OF ITERATED LOGARITHM FOR R/S STATISTICS

A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.

SOME LIMIT PROPERTIES OF LOCAL TIME FOR RANDOM WALK

Let X,X1,X2 be i. i. d. random variables with EX^2＋δ〈∞ （for some δ〉0）. Consider a one dimensional random walk S={Sn}n≥0, starting from S0 =0. Let ζ＊ （n）=supx∈zζ（x,n）,ζ（x,n） =#{0≤k≤n：[Sk]=x}. A strong approximation of ζ（n） by the local time for Wiener process is presented and the limsup type and liminf-type laws of iterated logarithm of the maximum local time ζ＊（n） are obtained. Furthermore,the precise asymptoties in the law of iterated logarithm of ζ＊（n） is proved.

STRONG PREDICTOR-CORRECTOR APPROXIMATION FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.

Review on non-dipole effects in ionization and harmonic generation of atoms and molecules

In this review,we will focus on recent progress on the investigations of nondipole effects in few-electron atoms and molecules interacting with light fields.We first briefly survey several popular theoretical methods and relevant concepts in strong field and attosecond physics beyond the dipole approximation.Physical phenomena stemming from the breakdown of the dipole approximation are then discussed in various topics,including the radiation pressure and photon-momentum transfer,the atomic stabilization,the dynamic interference,and the high-order harmonic generation.Whenever available,the corresponding experimental observations of these nondipole effects are also introduced respectively in each topics.