The Experts below are selected from a list of 25938 Experts worldwide ranked by ideXlab platform
Badong Chen - One of the best experts on this subject based on the ideXlab platform.
-
robust proportionate adaptive filter based on maximum correntropy criterion for sparse system identification in impulsive noise environments
Signal Image and Video Processing, 2018Co-Authors: Dongqiao Zheng, Zhiyu Zhang, Jiandong Duan, Badong ChenAbstract:Proportionate-type adaptive filtering (PtAF) algorithms have been successfully applied to sparse system identification. The major drawback of the traditional PtAF algorithms based on the mean Square error (MSE) criterion show poor robustness in the presence of impulsive noises or abrupt changes because MSE is only valid and rational under Gaussian assumption. However, this assumption is not satisfied in most real-world applications. To improve its robustness under non-Gaussian environments, we incorporate the maximum correntropy criterion (MCC) into the update equation of the PtAF to develop proportionate MCC (PMCC) algorithm. The mean and mean Square Convergence performance analysis are also performed. Simulation results in sparse system identification and echo cancellation applications are presented, which demonstrate that the proposed PMCC exhibits outstanding performance under the impulsive noise environments.
-
kernel risk sensitive loss definition properties and application to robust adaptive filtering
IEEE Transactions on Signal Processing, 2017Co-Authors: Badong Chen, Nanning Zheng, Lei Xing, Haiquan Zhao, Jose C PrincipeAbstract:Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean Square Convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster Convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.
-
general mixed norm based diffusion adaptive filtering algorithm for distributed estimation over network
IEEE Access, 2017Co-Authors: Jiandong Duan, Weishi Man, Junli Liang, Badong ChenAbstract:A diffusion general mixed-norm (DGMN) algorithm for distributed estimation over network (DEoN) is proposed. The standard diffusion adaptive filtering algorithm with a single error norm exhibits slow Convergence speed and poor misadjustments under specific environments. To overcome this drawback, the DGMN is developed by using a convex mixture of p and textit q norms as the cost function to improve the Convergence rate and substantially reduce the steady-state coefficient errors. Especially, it can be used to solve the DEoN under Gaussian and non-Gaussian noise environments, including measurement noises with long-tail and short-tail distributions, and impulsive noises with $\alpha $ -stable distributions. In addition, the analysis of the mean and mean Square Convergence is performed. Simulation results show the advantages of the proposed algorithm with mixing error norms for DEoN.
-
diffusion maximum correntropy criterion algorithms for robust distributed estimation
Digital Signal Processing, 2016Co-Authors: Badong Chen, Jiandong Duan, Haiquan ZhaoAbstract:Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adapt then combine MCC and combine then adapt MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean Square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, especially for the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power (DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean Square Convergence analysis of the new algorithms are also carried out.
-
diffusion maximum correntropy criterion algorithms for robust distributed estimation
arXiv: Machine Learning, 2015Co-Authors: Badong Chen, Jiandong Duan, Haiquan ZhaoAbstract:Robust diffusion adaptive estimation algorithms based on the maximum correntropy criterion (MCC), including adaptation to combination MCC and combination to adaptation MCC, are developed to deal with the distributed estimation over network in impulsive (long-tailed) noise environments. The cost functions used in distributed estimation are in general based on the mean Square error (MSE) criterion, which is desirable when the measurement noise is Gaussian. In non-Gaussian situations, such as the impulsive-noise case, MCC based methods may achieve much better performance than the MSE methods as they take into account higher order statistics of error distribution. The proposed methods can also outperform the robust diffusion least mean p-power(DLMP) and diffusion minimum error entropy (DMEE) algorithms. The mean and mean Square Convergence analysis of the new algorithms are also carried out.
T J Sullivan - One of the best experts on this subject based on the ideXlab platform.
-
strong Convergence rates of probabilistic integrators for ordinary differential equations
Statistics and Computing, 2019Co-Authors: Han Cheng Lie, Andrew M Stuart, T J SullivanAbstract:Probabilistic integration of a continuous dynamical system is a way of systematically introducing discretisation error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the Convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al. (Stat Comput 27(4):1065–1082, 2017. https://doi.org/10.1007/s11222-016-9671-0), to establish mean-Square Convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially bounded local Lipschitz constants all have the same mean-Square Convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.
-
strong Convergence rates of probabilistic integrators for ordinary differential equations
arXiv: Numerical Analysis, 2017Co-Authors: Han Cheng Lie, Andrew M Stuart, T J SullivanAbstract:Probabilistic integration of a continuous dynamical system is a way of systematically introducing model error, at scales no larger than errors introduced by standard numerical discretisation, in order to enable thorough exploration of possible responses of the system to inputs. It is thus a potentially useful approach in a number of applications such as forward uncertainty quantification, inverse problems, and data assimilation. We extend the Convergence analysis of probabilistic integrators for deterministic ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\ Comput.}, 2017), to establish mean-Square Convergence in the uniform norm on discrete- or continuous-time solutions under relaxed regularity assumptions on the driving vector fields and their induced flows. Specifically, we show that randomised high-order integrators for globally Lipschitz flows and randomised Euler integrators for dissipative vector fields with polynomially-bounded local Lipschitz constants all have the same mean-Square Convergence rate as their deterministic counterparts, provided that the variance of the integration noise is not of higher order than the corresponding deterministic integrator. These and similar results are proven for probabilistic integrators where the random perturbations may be state-dependent, non-Gaussian, or non-centred random variables.
Dmitriy F Kuznetsov - One of the best experts on this subject based on the ideXlab platform.
-
application of multiple fourier legendre series to implementation of strong exponential milstein and wagner platen methods for non commutative semilinear stochastic partial differential equations
arXiv: Probability, 2019Co-Authors: Dmitriy F KuznetsovAbstract:The article is devoted to the application of multiple Fourier-Legendre series to implementation of strong exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations with multiplicative trace class noise. These methods have strong orders of Convergence $1.0-\varepsilon$ and $1.5-\varepsilon$ correspondingly (here $\varepsilon$ is an arbitrary small positive real number) with respect to the temporal discretization. The theorem on mean-Square Convergence of approximations of iterated stochastic Ito integrals of multiplicities 1 to 3 with respect to the infinite-dimensional $Q$-Wiener process is formulated and proved. The results of the article can be applied to implementation of exponential Milstein and Wagner-Platen methods for non-commutative semilinear stochastic partial differential equations with multiplicative trace class noise.
-
on numerical modeling of the multidimensional dynamic systems under random perturbations with the 1 5 and 2 0 orders of strong Convergence
Automation and Remote Control, 2018Co-Authors: Dmitriy F KuznetsovAbstract:The paper was devoted to developing numerical methods with the orders 1.5 and 2.0 of strong Convergence for the multidimensional dynamic systems under random perturbations obeying stochastic differential Ito equations. Under the assumption of a special mean-Square Convergence criterion, attention was paid to the methods of numerical modeling of the iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 4 that are required to realize the aforementioned numerical methods.
-
expansion of iterated stochastic integrals with respect to martingale poisson measures and with respect to martingales based on generalized multiple fourier series
arXiv: Probability, 2018Co-Authors: Dmitriy F KuznetsovAbstract:We consider some versions and generalizations of the approach to expansion of iterated Ito stochastic integrals of arbitrary multiplicity $k$ $(k\in\mathbb{N})$ based on generalized multiple Fourier series. The expansions of iterated stochastic integrals with respect to martingale Poisson measures and with respect to martingales were obtained. For the iterated stochastic integrals with respect to martingales we have proved two theorems. The first theorem is the generalization of expansion for iterated Ito stochastic integrals of arbitrary multiplicity based on generalized multiple Fourier series. The second one is the modification of the first theorem for the case of complete orthonormal with weight $r(t_1)\ldots r(t_k)\ge 0$ systems of functions in the space $L_2([t, T]^k)$ (in the first theorem $r(t_1)\ldots r(t_k)\equiv 1$). Mean-Square Convergence of the considered expansions is proved. The example of expansion of iterated (double) stochastic integrals with respect to martingales with using the system of Bessel functions is considered.
-
direct combined approach for expansion of multiple stratonovich stochastic integrals of multiplicities 2 4 based on generalized multiple fourier series
arXiv: Probability, 2018Co-Authors: Dmitriy F KuznetsovAbstract:The article is devoted to the expansion of multiple Stratonovich stochastic integrals of multiplicities 2 - 4 on the base of the direct combined approach of generalized multiple Fourier series. We consider two different parts of the expansion of multiple Stratonovich stochastic integrals. The mean-Square Convergence of the first part is proven on the base of generalized multiple Fourier series, converging in $L_2([t, T]^k);$ $k=2, 3, 4.$ The mean-Square Convergence of the second part is proven on the base of generalized repeated Fourier series, converging pointwise. At that, we not use multiple Ito stochastic integrals as a tool of the proof and directly consider multiple Stratonovich stochastic integrals. The results of the article can be applied to numerical integration of Ito stochastic differential equations.
Xiaojie Wang - One of the best experts on this subject based on the ideXlab platform.
-
On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps
Numerical Algorithms, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-Square Convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahalia interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves the positivity of the original problem. Furthermore, we successfully recover the mean-Square Convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
-
mean Square Convergence rates of stochastic theta methods for sdes under a coupled monotonicity condition
Bit Numerical Mathematics, 2020Co-Authors: Xiaojie Wang, Bozhang DongAbstract:The present article revisits the well-known stochastic theta methods (STMs) for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. Under a coupled monotonicity condition in a domain $$D \subset {{\mathbb {R}}}^d, d \in {{\mathbb {N}}}$$ , we propose a novel approach to achieve upper mean-Square error bounds for STMs with the method parameters $$\theta \in [\tfrac{1}{2}, 1]$$ , which only get involved with the exact solution processes. This enables us to easily recover mean-Square Convergence rates of the considered schemes, without requiring a priori high-order moment estimates of numerical approximations. As applications of the error bounds, we derive mean-Square Convergence rates of STMs for SDEs driven by three kinds of noises under further globally polynomial growth condition. In particular, the error bounds are utilized to analyze approximation of SDEs with small noise. It is shown that the stochastic trapezoid formula gives better Convergence performance than the other STMs. Furthermore, we apply STMs to the Ait-Sahalia-type interest rate model taking values in the domain $$D = ( 0, \infty )$$ , and successfully identify a Convergence rate of order one-half for STMs with $$\theta \in [\tfrac{1}{2}, 1]$$ , even in a general critical case. This fills the gap left by Szpruch et al. (BIT Numer Math 51(2):405–425, 2011), where strong Convergence of the backward Euler method was proved, without revealing a rate of Convergence, for the model in a non-critical case.
-
mean Square Convergence rates of implicit milstein type methods for sdes with non lipschitz coefficients applications to financial models
arXiv: Numerical Analysis, 2020Co-Authors: Xiaojie WangAbstract:A novel class of implicit Milstein type methods is devised and analyzed in the present work for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffusion coefficients. By incorporating a pair of method parameters $\theta, \eta \in [0, 1]$ into both the drift and diffusion parts, the new schemes can be viewed as a kind of double implicit methods, which also work for non-commutative noise driven SDEs. Within a general framework, we offer upper mean-Square error bounds for the proposed schemes, based on certain error terms only getting involved with the exact solution processes. Such error bounds help us to easily analyze mean-Square Convergence rates of the schemes, without relying on a priori high-order moment estimates of numerical approximations. Putting further globally polynomial growth condition, we successfully recover the expected mean-Square Convergence rate of order one for the considered schemes with $\theta \in [\tfrac12, 1]$, solving general SDEs in various circumstances. As applications, some of the proposed schemes are also applied to solve two scalar SDE models arising in mathematical finance and evolving in the positive domain $(0, \infty)$. More specifically, the particular drift-diffusion implicit Milstein method ($ \theta = \eta = 1 $) is utilized to approximate the Heston $\tfrac32$-volatility model and the semi-implicit Milstein method ($\theta =1, \eta = 0$) is used to solve the Ait-Sahalia interest rate model. With the aid of the previously obtained error bounds, we reveal a mean-Square Convergence rate of order one of the positivity preserving schemes for the first time under more relaxed conditions, compared with existing relevant results for first order schemes in the literature. Numerical examples are finally reported to confirm the previous findings.
-
On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps.
arXiv: Numerical Analysis, 2020Co-Authors: Yuying Zhao, Xiaojie Wang, Mengchao WangAbstract:This article aims to reveal the mean-Square Convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main difficulty in the analysis is caused by the non-globally Lipschitz drift and diffusion coefficients of the model. We show that the BEM preserves positivity of the original problem. Furthermore, we successfully recover the mean-Square Convergence rate of order one-half for the BEM. The theoretical findings are accompanied by several numerical examples.
-
sharp mean Square regularity results for spdes with fractional noise and optimal Convergence rates for the numerical approximations
Bit Numerical Mathematics, 2017Co-Authors: Xiaojie Wang, Fengze JiangAbstract:This article offers sharp spatial and temporal mean-Square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infinite dimensional fractional Brownian motion with the Hurst parameter greater than one-half. In addition, the mean-Square numerical approximations of such problems are investigated, performed by the spectral Galerkin method in space and the linear implicit Euler method in time. The obtained sharp regularity properties of the problems enable us to identify optimal mean-Square Convergence rates of the full discrete scheme. These theoretical findings are accompanied by several numerical examples.
Siqing Gan - One of the best experts on this subject based on the ideXlab platform.
-
Convergence and stability of the backward euler method for jump diffusion sdes with super linearly growing diffusion and jump coefficients
Journal of Computational and Applied Mathematics, 2020Co-Authors: Ziheng Chen, Siqing GanAbstract:Abstract This paper firstly investigates Convergence of the backward Euler method for stochastic differential equations (SDEs) driven by Brownian motion and compound Poisson process. Different from existing works, we do not impose a globally Lipschitz condition on the jump coefficient but formulate a more relaxed condition to allow for its super-linear growth. It is shown that the mean Square Convergence order of this method can be arbitrarily close to 1 2 under mild assumptions imposed on SDEs, allowing for possibly super-linearly growing drift, diffusion and jump coefficients. An exact order 1 2 is recovered when further differentiability assumption is put on the coefficients. Furthermore, the considered method is able to inherit the mean Square stability of a wider class of Levy noise driven SDEs for all stepsizes. These results are finally supported by some numerical experiments.
-
mean Square Convergence of drift implicit one step methods for neutral stochastic delay differential equations with jump diffusion
Discrete Dynamics in Nature and Society, 2011Co-Authors: Siqing GanAbstract:A class of drift-implicit one-step schemes are proposed for the neutral stochastic delay differential equations (NSDDEs) driven by Poisson processes. A general framework for mean-Square Convergence of the methods is provided. It is shown that under certain conditions global error estimates for a method can be inferred from estimates on its local error. The applicability of the mean-Square Convergence theory is illustrated by the stochastic θ-methods and the balanced implicit methods. It is derived from Theorem 3.1 that the order of the mean-Square Convergence of both of them for NSDDEs with jumps is 1/2. Numerical experiments illustrate the theoretical results. It is worth noting that the results of mean-Square Convergence of the stochastic θ-methods and the balanced implicit methods are also new.
-
mean Square Convergence of stochastic θ methods for nonlinear neutral stochastic differential delay equations
2011Co-Authors: Siqing Gan, Henri Schurz, Haomin ZhangAbstract:This paper is devoted to the Convergence analysis of stochastic �-methods for non- linear neutral stochastic differential delay equations (NSDDEs) in Ito sense. The basic idea is to reformulate the original problem eliminating the dependence on the differentiation of the solution in the past values, which leads to a stochastic differential algebraic system. Drift-implicit stochas- tic �-methods are proposed for the coupled system. It is shown that the stochastic �-methods are mean-Square convergent with order 1 for Lipschitz continuous coefficients of underlying NSDDEs. A nonlinear numerical example illustrates the theoretical results.
-
mean Square Convergence of one step methods for neutral stochastic differential delay equations
Applied Mathematics and Computation, 2008Co-Authors: Haomin Zhang, Siqing GanAbstract:This paper deals with strong approximations of the solutions of neutral stochastic differential delay equations (NSDDEs) in Ito sense. A general framework for the strong Convergence of a class of drift-implicit one-step schemes to the solutions of NSDDEs is established. Two examples to illustrate the applicability of our results are provided.
