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On equivalence of state-based potential games

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Science China(Information Sciences) 2024年第6期67卷 313-327页

作者： Han WU Jinhuan WANG institute of mathematics School of ScienceHebei University of Technology

In this paper, we explore state-based potential games using the semi-tensor product of ***, applying the potential equation, we derive both a necessary and sufficient condition as well as a sufficient condition to verify whether a state-based game qualifies as a potential game. Next, we present two static equivalence conditions of state-based potential games. We then delve into dynamic equivalence. We propose a criterion that allows us to identify state-based games that are dynamically equivalent to state-based potential games and share similar dynamic properties. Ultimately, we introduce the concept of state-based networked evolutionary games. We provide a necessary and sufficient condition to ensure that a state-based networked evolutionary game can be classified as a state-based potential game.

关键词： semi-tensor product of matrices state-based potential game verification equivalence state-based networked evolutionary game

Identification of Linear Systems Using Binary Sensors with Random Thresholds

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Journal of Systems Science & Complexity 2024年第3期37卷 907-923页

作者： HUANG Zhiyong SONG Qijiang school of mathematics Renmin University of ChinaBeijing 100872China school of mathematics Sino-French InstituteRenmin University of ChinaBeijing 100872China

In this paper,the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is *** the help of stochastic approximation algorithms with expanding truncations,the authors give the recursive estimates for the parameters of both the linear system and the binary *** reasonable conditions,all constructed estimates are proved to be convergent to the true values with probability one,and the convergence rates are also established.A simulation example is provided to justify the theoretical results.

关键词： α-mixing binary sensor quantized system stochastic approximation stochastic thresh-old strongly consistent system identification

A DIRECT DISCONTINUOUS GALERKIN METHOD FOR TIME FRACTIONAL DIFFUSION EQUATIONS WITH FRACTIONAL DYNAMIC BOUNDARY CONDITIONS

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Journal of Computational mathematics 2024年第1期42卷 156-177页

作者： Jingjun Zhao Wenjiao Zhao Yang Xu school of mathematics Harbin Institute of TechnologyHarbin 150001China

This paper deals with the numerical approximation for the time fractional diffusion problem with fractional dynamic boundary *** well-posedness for the weak solutions is studied.A direct discontinuous Galerkin approach is used in spatial direction under the uniform meshes,together with a second-order Alikhanov scheme is utilized in temporal direction on the graded mesh,and then the fully discrete scheme is ***,the stability and the error estimate for the full scheme are analyzed in *** experiments are also given to illustrate the effectiveness of the proposed method.

关键词： Time fractional diffusion equation Numerical stability Convergence

A new two-step variational model for multiplicative noise removal with applications to texture images

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Applied mathematics(A Journal of Chinese Universities) 2024年第3期39卷 486-501页

作者： ZHANG Long-hui YAO Wen-juan SHI Sheng-zhu GUO Zhi-chang ZHANG Da-zhi school of mathematics Harbin Institute of TechnologyHarbin 150001China

Multiplicative noise removal problems have attracted much attention in recent *** additive noise,multiplicative noise destroys almost all information of the original image,especially for texture *** by the TV-Stokes model,we propose a new two-step variational model to denoise the texture images corrupted by multiplicative noise with a good geometry explanation in this *** the first step,we convert the multiplicative denoising problem into an additive one by the logarithm transform and propagate the isophote directions in the tangential field *** the isophote directions are constructed,an image is restored to fit the constructed directions in the second *** existence and uniqueness of the solution to the variational problems are *** these two steps,we use the gradient descent method and construct finite difference schemes to solve the ***,the augmented Lagrangian method and the fast Fourier transform are adopted to accelerate the *** results show that the proposed model can remove the multiplicative noise efficiently and protect the texture well.

关键词： multiplicative noise removal texture images total variation two-step variational method aug-mented Lagrangian method

MODIFIED SPLIT-STEP THETA METHOD FOR STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION

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Journal of Computational mathematics 2024年第5期42卷 1226-1245页

作者： Jingjun Zhao Hao Zhou Yang Xu school of mathematics Harbin Institute of TechnologyHarbin 150001China

For solving the stochastic differential equations driven by fractional Brownian motion,we present the modified split-step theta method by combining truncated Euler-Maruyama method with split-step theta *** the problem under a locally Lipschitz condition and a linear growth condition,we analyze the strong convergence and the exponential stability of the proposed ***,for the stochastic delay differential equations with locally Lipschitz drift condition and globally Lipschitz diffusion condition,we give the order of ***,numerical experiments are done to confirm the theoretical conclusions.

关键词： Stochastic differential equation Fractional Brownian motion Split-step theta method Strong convergence Exponential stability

On the convergence of tracking differentiator with multiple stochastic disturbances

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Science China(Information Sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG school of mathematics and Big Data Foshan University school of mathematics and Statistics Central South University Academy of mathematics and Systems Science Chinese Academy of Sciences Systems Engineering institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances

Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

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Chinese Physics B 2024年第9期33卷 340-348页

作者： Minfang Zhao Lingting Kong Miao Liu Shaoyong Lai school of mathematics and Statistics Yili Normal UniversityYining 835000China institute of Applied mathematics Yili Normal UniversityYining 835000China school of mathematics Southwestern University of Finance and EconomicsChengdu 611130China

The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,*** the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision *** steady-state solutions of the Fokker–Planck equation are obtained in exact *** experiments are provided to support our results under different parameters.

关键词： kinetic theory service time Fokker–Planck equation value function

The KAM theorem on the modulus of continuity about parameters

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Science China mathematics 2024年第3期67卷 577-592页

作者： Zhicheng Tong Jiayin Du Yong Li school of mathematics Jilin UniversityChangchun 130012China institute of mathematics Jilin UniversityChangchun 130012China school of mathematics and Statistics Center for Mathematics and Interdisciplinary SciencesNortheast Normal UniversityChangchun 130024China

In this paper,we study the Hamiltonian systems H(y,x,ξ,ε)=〈ω(ξ),y〉+εP(y,x,ξ,ε),where ω and P are continuous about ξ.We prove that persistent invariant tori possess the same frequency as the unperturbed tori,under a certain transversality condition and a weak convexity condition for the frequency mapping ω.As a direct application,we prove a Kolmogorov-Arnold-Moser(KAM) theorem when the perturbation P holds arbitrary Holder continuity with respect to the parameter ξ.The infinite-dimensional case is also *** our knowledge,this is the first approach to the systems with the only continuity in the parameter beyond H?lder's type.

关键词： Hamiltonian systems invariant tori frequency-preserving weak regularity

Irrational-Behavior-Proof Conditions for Stochastic Games over Event Trees

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Journal of the Operations Research Society of China 2024年第1期12卷 243-263页

作者： Lei Wang Cui Liu Hong-Wei Gao Chong Lin school of Automation Institute of Complexity ScienceQingdao UniversityQingdao 266071ShandongChina school of mathematics and Statistics Institute of Applied Mathematics of ShandongQingdao UniversityQingdao 266071ShandongChina

In this paper,the irrational-behavior-proof conditions in a class of stochastic dynamic games over event trees are *** kinds of irrational-behavior-proof conditions are proposed by the imputation distribution procedure,and their relationships are *** specific properties for the general transformation of characteristic functions are developed,based on which,the irrational-behavior-proof conditions are proved to be true in a transformed cooperative game.

关键词： Dynamic cooperative game Event tree Irrational-behavior-proof condition Imputation distribution procedure Transformation of characteristic function