Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is g...Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.展开更多
Let G = SU（n, 1）, K = S（U（n） × U（1））, and for l ∈Z, let {T;},l∈Z be a one- Dimensional K-type and let Et be the line bundle over G/K associated to Tl. In this work we obtain a central limit theorem for ...Let G = SU（n, 1）, K = S（U（n） × U（1））, and for l ∈Z, let {T;},l∈Z be a one- Dimensional K-type and let Et be the line bundle over G/K associated to Tl. In this work we obtain a central limit theorem for the space Et.展开更多
Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves t...Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.展开更多
A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding ...A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].展开更多
In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit th...In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.展开更多
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where s...Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| <∞and Rn = o(n^(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.展开更多
The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem ...The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.展开更多
Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a k...Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.展开更多
Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determin...Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.展开更多
The catalytic super_Brownian motion has been considered.If both the catalytic medium process Q and CSBM started with Lebesgue measureλ,the central limit theorem for occupation time of CSBM has been obtained in dimens...The catalytic super_Brownian motion has been considered.If both the catalytic medium process Q and CSBM started with Lebesgue measureλ,the central limit theorem for occupation time of CSBM has been obtained in dimension 3 for P-λ_a.s.Q.展开更多
In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then stud...In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.展开更多
文摘Let G = SU（2, 2）, K = S（U（2） × U（2））, and for l ∈ Z, let {Tl}l∈z be a one-dimensional K-type and let El be the line bundle over G/K associated to Tl. It is shown that the Tl-spherical function on G is given by the hypergeometric functions of several variables. By applying this result, a central limit theorem for the space G/K is obtained.
基金the National Natural Science Foundation of China(70271069)
文摘Let G = SU（n, 1）, K = S（U（n） × U（1））, and for l ∈Z, let {T;},l∈Z be a one- Dimensional K-type and let Et be the line bundle over G/K associated to Tl. In this work we obtain a central limit theorem for the space Et.
文摘Considering a sequence of standardized stationary Gaussian random variables, a universal result in the almost sure central limit theorem for maxima and partial sum is established. Our result generalizes and improves that on the almost sure central limit theory previously obtained by Marcin Dudzinski [1]. Our result reaches the optimal form.
基金the National Natural Science Foundation of China(No.10271087).
文摘A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].
基金Supported by grants from the NSF of China(Grant No.11731012,12031005)Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042)+1 种基金NSF of Zhejiang Province(Grant No.LZ21A010002)the Fundamental Research Funds for the Central Universities.
文摘In this paper,the functional central limit theorem is established for martingale like ran-dom vectors under the framework sub-linear expectations introduced by Shige Peng.As applications,the Lindeberg central limit theorem for independent random vectors is established,the sufficient and necessary conditions of the central limit theorem for independent and identically distributed random vectors are found,and a Lévy’s characterization of a multi-dimensional G-Brownian motion is obtained.
基金This work was partially supported by the Natural Science Foundation of Zhejiang Province(Grant No.101016)the National Natural Science Foundation of China(Grant No.10471126).
文摘Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn + Rn, where supn E|Rn| <∞and Rn = o(n^(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc.
基金supported by National Natural Science Foundation of China(Grant No.11731012)the Fundamental Research Funds for the Central Universities+1 种基金the State Key Development Program for Basic Research of China(Grant No.2015CB352302)Zhejiang Provincial Natural Science Foundation(Grant No.LY17A010016)。
文摘The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes,especially stochastic integrals and differential equations.In this paper,the central limit theorem and the functional central limit theorem are obtained for martingale-like random variables under the sub-linear expectation.As applications,the Lindeberg's central limit theorem is obtained for independent but not necessarily identically distributed random variables,and a new proof of the Lévy characterization of a GBrownian motion without using stochastic calculus is given.For proving the results,Rosenthal's inequality and the exponential inequality for the martingale-like random variables are established.
文摘Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions.
基金the Shanghai Science and Technology Commission, No. 01ZA14003.
文摘Various properties of the characteristic functions of random variables in a non-commutative C*-probability space are studied in this paper. It turns out that the distributions of random variables are uniquely determined by their characteristic functions. By using the properties of characteristic functions, a central limit theorem for a sequence of independent identically distributed random variables in a C*-probability space is established as well.
基金sup-ported by the National Nat ural Science Foundation of China(Grant No.19671011)the Mathematical Centre of State Education Commission.
文摘The catalytic super_Brownian motion has been considered.If both the catalytic medium process Q and CSBM started with Lebesgue measureλ,the central limit theorem for occupation time of CSBM has been obtained in dimension 3 for P-λ_a.s.Q.
文摘为适应下一代微功率无线抄表技术发展的需要,针对470~510 MHz特定频段在室内和室外环境中进行信道特性测量并提取信道特性参数,建立路径损耗模型。测量过程中,发射端使用SMW200A矢量信号发生器发送信号,利用频域测量系统的扫频测量法,在室内办公室环境和室外郊区环境中抓取测量数据,同时考虑信号在室内传输过程中墙壁、门窗开闭以及室外行人、车辆、树木等障碍物的影响,分析其大尺度衰落特性。根据测量数据,利用最小二乘法和中心极限定理估算路径损耗模型中的路径损耗因子 n 和标准偏差σ,得出在室内视距情况下470~510 MHz频段的路径损耗模型和室外郊区空旷地带的路径损耗模型。测量和仿真结果表明,该路径损耗模型能较好地预测接收信号强度,为后续测量和抄表业务部署提供依据。
基金the National Natural Science Foundation of China (Grant No.10121101)
文摘In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue measure.We first prove a functional central limit theorem,and then study the large and moderate deviations associated with this central tendency.
