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Stabilization for multi-group coupled stochastic models by delay feedback control and nonlinear impulsive control

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Science China(Information Sciences) 2018年第7期61卷 119-129页

作者： Chaolong ZHANG Feiqi DENG Yiping LUO Department of Computational Science Zhongkai University of Agriculture and Engineering Systems Engineering Institute South China University of Technology College of Electrical and Information Engineering Hunan Institute of Engineering

Stabilization for multi-group coupled models stochastic by delay feedback control and nonlinear impulsive control are considered in this paper. Using graph theory and Lyapunov method, some sufficient conditions are acquired by some control methods. Those criteria are easier to verify and no need to solve any linear matrix inequalities. These results can be designed more easily in practice. At last, the effectiveness and advantage of the theoretical results are verified by an example.

关键词： stabilization graph theory stochastic impulsive delay

Forward and Backward Mean-Field stochastic Partial Differential Equation and Optimal Control

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Chinese Annals of Mathematics,Series B 2019年第4期40卷 515-540页

作者： Maoning TANG Qingxin MENG Meijiao WANG Department of Mathematical Sciences Huzhou UniversityHuzhou 313000ZhejiangChina Department of Mathematical Sciences Huzhou UniversityHuzhou 313000ZhejiangChina Business School University of Shanghai for Science and TechnologyShanghai 200093China

This paper is mainly concerned with the solutions to both forward and backward mean-field stochastic partial differential equation and the corresponding optimal control problem for mean-field stochastic partial differential equation. The authors first prove the continuous dependence theorems of forward and backward mean-field stochastic partial differential equations and show the existence and uniqueness of solutions to them. Then they establish necessary and sufficient optimality conditions of the control problem in the form of Pontryagin’s maximum principles. To illustrate the theoretical results, the authors apply stochastic maximum principles to study the infinite-dimensional linear-quadratic control problem of mean-field type. Further, an application to a Cauchy problem for a controlled stochastic linear PDE of mean-field type is studied.

关键词： Mean-field stochastic partial differential equation Backward stochastic partial differential equation Optimal control Maximum principle Adjoint equation

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The effect of micro-structural uncertainties of recycled aggregate concrete on its global stochastic properties via finite pixel-element Monte Carlo simulation

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Frontiers of Structural and Civil Engineering 2018年第4期12卷 474-489页

作者： Qingpeng MENG Yuching WU Jianzhuang XIAO Department of Structural Engineering College of Civil EngineeringTongji UniversityShanghai 200092China

In this paper, the effect of micro-structural uncertainties of recycled aggregate concrete (RAC) on its global stochastic elastic properties is investigated via finite pixel-element Monte Carlo simulation. Representative RAC models are randomly generated with various distribution of aggregates. Based on homogenization theory, effects of recycled aggregate replacement rate, aggregate volume fraction, the unevenness of old mortar, proportion of old mortar, aggregate size and elastic modulus of aggregates on overall variability of equivalent elastic properties are investigated. Results are in a good agreement with experimental data in literature and finite pixel-element method saves the computation cost. It is indicated that the effect of mesoscopic randomness on global variability of elastic properties is considerable.

关键词： RAC Monte Carlo analysis stochastic finite pixel-element method homogenization coefficient of variation recycled-aggregate concrete stochastic Elastic properties Experimental data Monte Carlo technique AKT1 gene aggregates homogenization COEFFICIENT OF VARIATION

STABILITY OF THE stochastic θ-METHOD FOR SUPER-LINEAR stochastic DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

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Journal of Computational Mathematics 2019年第5期37卷 704-720页

作者： Lin Chen School of Statistics Jiangxi University of Finance and Economics Nanchang 330013China Research Center of Applied Statistics Jiangxi University of Finance and Economics Nanchang 330013China

This paper deals with numerical stability properties of super-linear stochastic differential equations with unbounded delay. Sufficient conditions for mean square and almost sure decay stability of the above system and its stochastic θ-method approximation are investigated in this paper. The author establishes numerical stability under a monotone-type condition in unbounded delay setting. An example is presented to illustrate the result.

关键词： Unbounded delay Monotone condition Polynomial condition stochastic θ- method Decay stability.

Transient measurement of phononic states with covariance-based stochastic spectroscopy

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Light(Science & Applications) 2022年第3期11卷 68-75页

作者： Giorgia Sparapassi Stefano MCavaletto Jonathan Tollerud Angela Montanaro Filippo Glerean Alexandre Marciniak Fancesca Giusti Shaul Mukamel Daniele Fausti Physics Department University of TriesteTriesteItaly Elettra-Sincrotrone Trieste S.C.p.A. TriesteItaly Department of Chemistry and Department of Physics&Astronomy University of CaliforniaIrvineCAUSA Optical Sciences Centre Swinburne UniversityMelbourneAustralia

We present a novel approach to transient Raman spectroscopy,which combines stochastic probe pulses and a covariance-based detection to measure stimulated Raman signals in alpha-quartz.A coherent broadband pump is used to simultaneously impulsively excite a range of different phonon modes,and the phase,amplitude,and energy of each mode are independently recovered as a function of the pump-probe delay by a noisy-probe and covariance-based analysis.Our experimental results and the associated theoretical description demonstrate the feasibility of 2D-Raman experiments based on the stochastic-probe schemes,with new capabilities not available in equivalent mean-value-based 2D-Raman techniques.This work unlocks the gate for nonlinear spectroscopies to capitalize on the information hidden within the noise and overlooked by a mean-value analysis.

关键词： stochastic spectroscopy coherent

NONLINEAR stochastic HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY

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Acta Mathematica Scientia 2019年第3期39卷 645-668页

作者：陈乐 Kunwoo KIM Department of Mathematical Sciences University of NevadaLas Vegas4505 S.Maryland PkwyLas VegasNevada89154-4020USA Department of Mathematics Pohang University of Science and Technology77 Cheongam-RoNam-GuPohangGyeongbuk37673Korea

In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.

关键词： stochastic heat equation moment estimates phase transition intermittency intermittency front measure-valued initial data moment Lyapunov exponents

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Exis tence and st ability of μ-pseudo almost automorphic solutions for stochastic evolution equations

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Frontiers of Mathematics in China 2019年第2期14卷 261-280页

作者： Jing CUI Wenping RONG College of Mathematics and Statistics Anhui Normal University Wuhu 241000 China

We introduce a new concept of μ-pseudo almost automorphic processes in p-th mean sense by employing the measure theory, and present some results on the functional space of such processes like completeness and composition theorems. Under some conditions, we establish the existence, uniqueness, and the global exponentially stability of μ-pseudo almost automorphic mild solutions for a class of nonlinear stochastic evolution equations driven by Brownian motion in a separable Hilbert space.

关键词： stochastic evolution equation μ-pseudo almost automorphic process fixed point theorem

NUMERICAL SOLUTIONS OF NONAUTONOMOUS stochastic DELAY DIFFERENTIAL EQUATIONS BY DISCONTINUOUS GALERKIN METHODS

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Journal of Computational Mathematics 2019年第3期37卷 419-436页

作者： Xinjie Dai Aiguo Xiao School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105China School of Mathematics and Computational Science & Hunan Key Laboratory for Computation and Simulation in Science and Engineering Xiangtan UniversityXiangtan 411105China

This paper considers a class of discontinuous Galerkin method,which is constructed by Wong-Zakai approximation with the orthonormal Fourier basis,for numerically solving nonautonomous Stratonovich stochastic delay differential equations.We prove that the discontinuous Galerkin scheme is strongly convergent:globally stable and analogously asymptotically stable in mean square sense.In addition,this method can be easily extended to solve nonautonomous Stratonovich stochastic pantograph differential equations.Numerical tests indicate that the method has first-order and half-order strong mean square convergence,when the diffusion term is without delay and with delay,respectively.

关键词： Discontinuous Galerkin method Wong-Zakai approximation Nonautonomous Stratonovich stochastic delay differential equation

DESCENT DIRECTION stochastic APPROXIMATION ALGORITHM WITH ADAPTIVE STEP SIZES

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Journal of Computational Mathematics 2019年第1期37卷 76-94页

作者： Zorana Luzanin Irena Stojkovska Milena Kresoja Department of Mathematics and Informatics Faculty of SciencesUniversity of Novi Sad Novi SadSerbia Department of Mathematics.Faculty of Natural Sciences and Mathematics Ss.Cyril and Methodius UniversitySkopjeMacedonia

A stochastic approximation (SA)algorithm with new adaptive step sizes for solving unconstrained minimization problems in noisy environment is proposed.New adaptive step size scheme uses ordered statistics of fixed number of previous noisy function values as a criterion for accepting good and rejecting bad steps.The scheine allows the algorithm to move in bigger steps and avoid steps proportional to 1/k when it is expected that larger steps will improve the performance.An algorithin with the new adaptive scheme is defined for a general descent direction.The ahnost sure convergence is established.The performance of new algorithm is tested on a set of standard test problems and compared with relevant algorithms.Numerical results support theoretical expectations and verify efficiency of the algorithm regardless of chosen search direction and noise level.Numerical results on probleins arising in machine learning are also presented.Linear regression problem is considered using real data set.The results suggest that the proposed algorithln shows proinise.

关键词： Unconstrained optimization stochastic optimization stochastic approximation Noisy function Adaptive step size Descent direction Linear regression model