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 dependen...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.展开更多
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.
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) den...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.…展开更多
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,wo...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.展开更多
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...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.展开更多
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 ^...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.展开更多
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 ...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.展开更多
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 ar...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.展开更多
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.
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 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 ...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.展开更多
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 s...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.展开更多
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...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.展开更多
This paper proposes a modified strong field approximation model for evaluating nondipole effects on the ionization of an atom in an intense laser field. The photoelectron longitudinal momentum distributions (PLMD) o...This paper proposes a modified strong field approximation model for evaluating nondipole effects on the ionization of an atom in an intense laser field. The photoelectron longitudinal momentum distributions (PLMD) of a hydrogen-like atom exposed to a mid-infrared laser field is calculated. The theoretical results indicate an obvious asymmetry in the PLMD, and an offset of the PLMD peak appears in the opposite direction of the beam propagation due to nondipole effects. The peak offsets of the PLMD increased with the laser intensity, imposed by the initial state of the hydrogen-like atom.展开更多
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 ...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.展开更多
We derive a simple ionization rate formula for the ground state of a hydrogen atom in the velocity gauge under the conditions:ω〈〈1 a.u.(a.u.is short for atomic unit) and γ〈〈1(ω is the laser frequency and y ...We derive a simple ionization rate formula for the ground state of a hydrogen atom in the velocity gauge under the conditions:ω〈〈1 a.u.(a.u.is short for atomic unit) and γ〈〈1(ω is the laser frequency and y is the Keldysh parameter).Comparisons are made among the different versions of the Keldysh-Faisal-Reiss(KFR) theory.The numerical study shows that with considering the quasi-classical(WKB) Coulomb correction in the final state of the ionized electron,the photoionization rate is enhanced compared with without considering the Coulomb correction,and the Reiss theory with the WKB Coulomb correction gives the correct result in the tunneling regime.Our concise formula of the ionization rate may provide an insight into the ionization mechanism for the ground state of a hydrogen atom.展开更多
The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arri...The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.展开更多
Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤...Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).展开更多
文摘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.
文摘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.
基金Supported by NSF of China, under the Grant 10471010.
文摘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.…
基金supported by the National Natural Science Foundation of China(No.11871116 and No.11971074)by the Fundamental Research Funds for the Central Universities(No.2023ZCJH02)。
文摘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.
基金Supported by The National Natural Science Foundation of China (No.10071072)
文摘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.
基金Supported by National Natural Science Foundation of China(No.10071072)
文摘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.
基金NSFC (10401037) China Postdoctoral Science Foundation
文摘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.
文摘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.
基金National Natural Science Foundation of China(Grant Nos.11622111,11631009,11621061 and 11688101)。
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No. 10871177)Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 20090101110020)
文摘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.
文摘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.
基金Project Supported by NSFC (10131040)SRFDP (2002335090)
文摘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.
文摘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.
基金This work is supported by National Natural Science Foundation of China (Nos. 11401594, 11171125, 91130003) and the New Teachers' Specialized Research Fund for the Doctoral Program from Ministry of Education of China (No. 20120162120096).
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.11274149)the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology,China(Grant No.F12-254-1-00)
文摘This paper proposes a modified strong field approximation model for evaluating nondipole effects on the ionization of an atom in an intense laser field. The photoelectron longitudinal momentum distributions (PLMD) of a hydrogen-like atom exposed to a mid-infrared laser field is calculated. The theoretical results indicate an obvious asymmetry in the PLMD, and an offset of the PLMD peak appears in the opposite direction of the beam propagation due to nondipole effects. The peak offsets of the PLMD increased with the laser intensity, imposed by the initial state of the hydrogen-like atom.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11961131008,11725416,and 11574010)the National Key Research and Development Program of China(Grant No.2018YFA0306302)
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11274149 and 11304185)the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology,China(Grant No.F12-254-1-00)
文摘We derive a simple ionization rate formula for the ground state of a hydrogen atom in the velocity gauge under the conditions:ω〈〈1 a.u.(a.u.is short for atomic unit) and γ〈〈1(ω is the laser frequency and y is the Keldysh parameter).Comparisons are made among the different versions of the Keldysh-Faisal-Reiss(KFR) theory.The numerical study shows that with considering the quasi-classical(WKB) Coulomb correction in the final state of the ionized electron,the photoionization rate is enhanced compared with without considering the Coulomb correction,and the Reiss theory with the WKB Coulomb correction gives the correct result in the tunneling regime.Our concise formula of the ionization rate may provide an insight into the ionization mechanism for the ground state of a hydrogen atom.
基金supported by the National Natural Science Foundation of China(No.11871116 and No.11971074).
文摘The law of the iterated logarithm(LIL)for the performance measures of a two-station queueing network with arrivals modulated by independent queues is developed by a strong approximation method.For convenience,two arrival processes modulated by queues comprise the external system,all others are belong to the internal system.It is well known that the exogenous arrival has a great influence on the asymptotic variability of performance measures in queues.For the considered queueing network in heavy traffic,we get all the LILs for the queue length,workload,busy time,idle time and departure processes,and present them by some simple functions of the primitive data.The LILs tell us some interesting insights,such as,the LILs of busy and idle times are zero and they reflect a small variability around their fluid approximations,the LIL of departure has nothing to do with the arrival process,both of the two phenomena well explain the service station’s situation of being busy all the time.The external system shows us a distinguishing effect on the performance measures:an underloaded(overloaded,critically loaded)external system affects the internal system through its arrival(departure,arrival and departure together).In addition,we also get the strong approximation of the network as an auxiliary result.
基金Supported by National Natural Science Foundation of China (No. 10071072)
文摘Let {X, X_; ∈N^d} be a field of i.i.d, random variables indexed by d-tuples of positive integers and taking values in a Banach space B and let X_^((r))=X_(m) if ‖X_‖ is the r-th maximum of {‖X_‖; ≤. Let S_=∑(≤)X_ and ^((r))S_=S_-(X_^((1))+…+X_^((r)). We approximate the trimmed sums ^((r))_n, by a Brownian sheet and obtain sufficient and necessary conditions for ^((r))S_ to satisfy the compact and functional laws of the iterated logarithm. These results improve the previous works by Morrow (1981), Li and Wu (1989) and Ledoux and Talagrand (1990).