This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional...This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional Lower Order Statistics (FLOS). Unlike previously introduced FLOS-type algorithms, the new algorithm is proposed to estimate the time delay by maximizing the generalized correlation function of two observed signals needing neither prior information nor estimation of the numerical value of the stable noise's characteristic exponent. An interval for kernel selection is found for a wide range of characteristic exponent values of α-Stable distribution. Simulations show the proposed algorithm offers superior performance over the existing covariation time delay estimation, least mean p-norm time delay estimation and achieves slightly improved performance than fractional lower order covariance time delay estimation at lower signal to noise ratio when the noise is highly impulsive.展开更多
In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of...In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.展开更多
Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetric...Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.展开更多
Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measur...Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.展开更多
The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional ...The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.展开更多
We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution co...We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.展开更多
In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src=&...In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of L<sup>p</sup> p-harmonic 1-forms on M<sup>m</sup>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.展开更多
A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (...A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.展开更多
In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations....In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations. Our result is an extension of Cox and Griffeath’s (in 1985) for branching Brownian motion for d > 4.展开更多
We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, whe...We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x)=(1+|x|)β with β>α we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.展开更多
This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive ...This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.展开更多
基金Supported by the Chinese National Science Foundation(No.60872122)
文摘This paper presents a robust time delay estimation algorithm for the α-Stable noise based on correntropy. Many time delay estimation algorithms derived for impulsive stable noise are based on the theory of Fractional Lower Order Statistics (FLOS). Unlike previously introduced FLOS-type algorithms, the new algorithm is proposed to estimate the time delay by maximizing the generalized correlation function of two observed signals needing neither prior information nor estimation of the numerical value of the stable noise's characteristic exponent. An interval for kernel selection is found for a wide range of characteristic exponent values of α-Stable distribution. Simulations show the proposed algorithm offers superior performance over the existing covariation time delay estimation, least mean p-norm time delay estimation and achieves slightly improved performance than fractional lower order covariance time delay estimation at lower signal to noise ratio when the noise is highly impulsive.
基金This work was supported by the Key International(Regional)Joint Research Program of the National Natural Science Foundation of China(No.12120101002).
文摘In this paper,the path integral solutions for a general n-dimensional stochastic differential equa-tions(SDEs)withα-stable Lévy noise are derived and verified.Firstly,the governing equations for the solutions of n-dimensional SDEs under the excitation ofα-stable Lévy noise are obtained through the characteristic function of stochastic processes.Then,the short-time transition probability density func-tion of the path integral solution is derived based on the Chapman-Kolmogorov-Smoluchowski(CKS)equation and the characteristic function,and its correctness is demonstrated by proving that it satis-fies the governing equation of the solution of the SDE,which is also called the Fokker-Planck-Kolmogorov equation.Besides,illustrative examples are numerically considered for highlighting the feasibility of the proposed path integral method,and the pertinent Monte Carlo solution is also calculated to show its correctness and effectiveness.
基金supported by National Key R&D Program of China(Grant No.2018YFF01012600)National Natural Science Foundation of China(Grant No.61701021)Fundamental Research Funds for the Central Universities(Grant No.FRF-TP-19-006A3).
文摘Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.
基金Supported by NNSF of China (10001020 and 10471003), Foundation for Authors Awarded Excellent Ph.D.Dissertation
文摘Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.
基金Key Natural Science Foundation of Anhui Education Commission,China(No.KJ2017A568)Natural Science Foundation of Anhui Province,China(No.1808085MA02)+1 种基金Quality Engineering Project of Anhui Province,China(No.2019jyxm0476)Quality Engineering Project of Bengbu University,China(No.2018JYXML8)。
文摘The asymptotic behaviors for estimators of the drift parameters in the Ornstein-Uhlenbeck process driven by small symmetricα-stable motion are studied in this paper.Based on the discrete observations,the conditional least squares estimators(CLSEs)of all the parameters involved in the Ornstein–Uhlenbeck process are proposed.We establish the consistency and the asymptotic distributions of our estimators asεgoes to 0 and n goes to∞simultaneously.
基金Supported by the Science and Technology Research Projects of Hubei Provincial Department of Education(B2022077)。
文摘We study the distribution limit of a class of stochastic evolution equation driven by an additive-stable Non-Gaussian process in the case of α∈(1,2).We prove that,under suitable conditions,the law of the solution converges weakly to the law of a stochastic evolution equation with an additive Gaussian process.
文摘In this paper, we investigate the space of L<sup>p</sup> p-harmonic 1-forms on a complete noncompact orientable δ-stable hypersurface M<sup>m</sup> that is immersed in space form <img src="Edit_6fbc11b9-ac23-40e2-b045-0fb25419337d.png" width="35" height="23" alt="" /> with nonnegative BiRic curvature. We prove the nonexistence of L<sup>p</sup> p-harmonic 1-forms on M<sup>m</sup>. Moreover, we obtain some vanishing properties for this class of harmonic 1-forms.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.10101005 and 10121101)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry.
文摘A functional central limit theorem is proved for the centered occupation time process of the super α-stable processes in the finite dimensional distribution sense. For the intermediate dimensions α < d < 2α (0 < α ≤ 2), the limiting process is a Gaussian process, whose covariance is specified; for the critical dimension d= 2α and higher dimensions d < 2α, the limiting process is Brownian motion.
基金supported by National Natural Science Foundation of China (Grant Nos. 10971003 and 10926110)Chinese Universities Scientific Fund (Grant No. 2009-2-05)+1 种基金supported by National Natural Science Foundation of China (Grant Nos. 10871103 and 10971003)Specialized Research Fund for the Doctoral Program of Higher Education
文摘In this paper we establish a large deviation principle for the occupation times of critical branching α-stable processes for large dimensions d > 2α, by investigating two related nonlinear differential equations. Our result is an extension of Cox and Griffeath’s (in 1985) for branching Brownian motion for d > 4.
文摘We establish sharp functional inequalities for time-changed symmetric α-stable processes on Rd with d≥1 and α∈(0,2), which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function W(x)=(1+|x|)β with β>α we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups.
基金supported in part by the National Natural Science Foundation of China(61301228,61371091)the Fundamental Research Funds for the Central Universities(3132014212)
文摘This paper is mainly to deal with the problem of direction of arrival(DOA) estimations of multiple narrow-band sources impinging on a uniform linear array under impulsive noise environments. By modeling the impulsive noise as α-stable distribution, new methods which combine the sparse signal representation technique and fractional lower order statistics theory are proposed. In the new algorithms, the fractional lower order statistics vectors of the array output signal are sparsely represented on an overcomplete basis and the DOAs can be effectively estimated by searching the sparsest coefficients. To enhance the robustness performance of the proposed algorithms,the improved algorithms are advanced by eliminating the fractional lower order statistics of the noise from the fractional lower order statistics vector of the array output through a linear transformation. Simulation results have shown the effectiveness of the proposed methods for a wide range of highly impulsive environments.
