We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.
Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help...Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.展开更多
In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between v...In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.展开更多
In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {...In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.展开更多
Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present...Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.展开更多
Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important ineq...Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important inequal-ities, the value distribution of the Dirichlet series is studied where {Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn = 0; Xn or ReXn or ImAn of bounded density. Thereexists α> 0 such that Vn : (the classic Gauss and Steinhaus random variables are special cases of such random variables). The important results are obtained that every point on the line Res = 0 is a Picard point of the series without finite exceptional value a.s..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
This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in...This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.展开更多
A time-correlated random field bescribing the general flow is defined. A time-correlated functionalequation governing the evolution of its characteristic functional is derived.
通过大涡模拟(Large Eddy Simulation,LES)湍流求解方法和概率密度函数输运方程(Transported Probability Density Function,TPDF)湍流燃烧求解方法结合,对煤油燃料双旋流燃烧室(Gas Turbine Model Combustor,GTMC)进行了模拟,并利用经...通过大涡模拟(Large Eddy Simulation,LES)湍流求解方法和概率密度函数输运方程(Transported Probability Density Function,TPDF)湍流燃烧求解方法结合,对煤油燃料双旋流燃烧室(Gas Turbine Model Combustor,GTMC)进行了模拟,并利用经验模态分解(Empirical Mode Decomposition,EMD)和快速傅里叶变换(Fast Fourier Transform,FFT)等方法分析了GTMC的温度和速度非定常特性,获得了脉动主频的空间分布。结果显示:空间坐标为(2 cm,0 cm,3 cm)的特征点的温度主频为47和761 Hz;对本征模态函数(Intrinsic Mode Function,IMF)进行显著性分析,能量密度最高的IMF的主频即原始数据的主频;温度脉动主要受湍流流动影响;根据瑞利数场,热-压力激发与抑制区域总是交替出现。展开更多
八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定...八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定义失效,且现有研究多聚焦四元数域,缺乏三维OOLCT(3D-OOLCT)域的严谨概率框架。本文将基础概率理论引入3D-OOLCT领域,构建兼容八元数特性的概率体系:首先,定义3D-OOLCT域中八元数值概率密度函数、分布函数、均值及特征函数;其次,证明特征函数定理;最后,通过算例推导验证特定概率密度函数在3D-OOLCT域的特征函数表达式。该研究填补OOLCT域与概率理论结合的空白,完善八元数变换理论,为三维高维随机信号统计分析提供新工具,也为后续相关工程应用奠定数理基础。展开更多
针对电容式电压互感器(capacitor voltage transformer,CVT)的谐波传递特性,综合考虑杂散电容等因素影响,建立等效电路模型,采用逐级计算各级等效阻抗和传递函数的方法,对CVT谐波传递特性进行深入计算和分析。基于Matlab/Simulink仿真...针对电容式电压互感器(capacitor voltage transformer,CVT)的谐波传递特性,综合考虑杂散电容等因素影响,建立等效电路模型,采用逐级计算各级等效阻抗和传递函数的方法,对CVT谐波传递特性进行深入计算和分析。基于Matlab/Simulink仿真工具对CVT谐波传递特性开展了仿真验证,并针对实际CVT开展了CVT谐波传递特性和测量误差的实际物理试验研究,试验结果与仿真分析结果具有较好的一致性。发现影响CVT谐波传递特性的因素不仅是LC串联谐振回路额定工作点的偏移,中间变压器一次侧和补偿电抗器的杂散电容对CVT谐波传递特性有着重要影响,传递函数幅频特性曲线呈现尖峰和低谷效应,导致较大的测量误差。展开更多
基金The NSF (19971029) of China abd the Guangdong Provincial NSF (990444) of China.
文摘We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.
文摘Bilinear time series models are of importance to nonlinear time seriesanalysis.In this paper,the autocovariance function and the relation between linearand general bilinear time series models are derived.With the help of Volterra seriesexpansion,the impulse response function and frequency characteristic function of thegeneral bilinear time series model are also derived.
文摘In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.
基金Supported by the National Natural Science Foundation of China（10471048）
文摘In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.
基金supported by the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10902068,51121063 and 10702039)+1 种基金the Shanghai Pujiang Program (10PJ1406000)the Opening Project of State Key Laboratory of Mechanical System and Vibration (MSV201103)
文摘Volterra series is a powerful mathematical tool for nonlinear system analysis,and there is a wide range of nonlinear engineering systems and structures that can be represented by a Volterra series model.In the present study,the random vibration of nonlinear systems is investigated using Volterra series.Analytical expressions were derived for the calculation of the output power spectral density（PSD） and input-output cross-PSD for nonlinear systems subjected to Gaussian excitation.Based on these expressions,it was revealed that both the output PSD and the input-output crossPSD can be expressed as polynomial functions of the nonlinear characteristic parameters or the input intensity.Numerical studies were carried out to verify the theoretical analysis result and to demonstrate the effectiveness of the derived relationship.The results reached in this study are of significance to the analysis and design of the nonlinear engineering systems and structures which can be represented by a Volterra series model.
文摘Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important inequal-ities, the value distribution of the Dirichlet series is studied where {Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn = 0; Xn or ReXn or ImAn of bounded density. Thereexists α> 0 such that Vn : (the classic Gauss and Steinhaus random variables are special cases of such random variables). The important results are obtained that every point on the line Res = 0 is a Picard point of the series without finite exceptional value a.s..
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.
文摘This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.
基金The rescarch supported by the Chinese Postdoctoral Fund.
文摘A time-correlated random field bescribing the general flow is defined. A time-correlated functionalequation governing the evolution of its characteristic functional is derived.
文摘八元数偏移线性正则变换(octonion offset linear canonical transform,OOLCT)作为八元数线性正则变换(octonion linear canonical transform,OLCT)的推广形式,在高维非平稳信号时频调控中具有优势,但八元数非结合性使传统概率统计量定义失效,且现有研究多聚焦四元数域,缺乏三维OOLCT(3D-OOLCT)域的严谨概率框架。本文将基础概率理论引入3D-OOLCT领域,构建兼容八元数特性的概率体系:首先,定义3D-OOLCT域中八元数值概率密度函数、分布函数、均值及特征函数;其次,证明特征函数定理;最后,通过算例推导验证特定概率密度函数在3D-OOLCT域的特征函数表达式。该研究填补OOLCT域与概率理论结合的空白,完善八元数变换理论,为三维高维随机信号统计分析提供新工具,也为后续相关工程应用奠定数理基础。
文摘针对电容式电压互感器(capacitor voltage transformer,CVT)的谐波传递特性,综合考虑杂散电容等因素影响,建立等效电路模型,采用逐级计算各级等效阻抗和传递函数的方法,对CVT谐波传递特性进行深入计算和分析。基于Matlab/Simulink仿真工具对CVT谐波传递特性开展了仿真验证,并针对实际CVT开展了CVT谐波传递特性和测量误差的实际物理试验研究,试验结果与仿真分析结果具有较好的一致性。发现影响CVT谐波传递特性的因素不仅是LC串联谐振回路额定工作点的偏移,中间变压器一次侧和补偿电抗器的杂散电容对CVT谐波传递特性有着重要影响,传递函数幅频特性曲线呈现尖峰和低谷效应,导致较大的测量误差。
