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Stochastic Averaging Principle for Neutral Stochastic Functional Differential Equations Driven by G-Levy Process G-Levy 过程驱动的中性随机函数微分方程的随机平均原理
IF 0.8 4区 数学
Stochastics and Dynamics Pub Date : 2024-07-25 DOI: 10.1142/s0219493724500291
Guangjun Shen, Jingjing Fan, Jiang-Lun Wu, Zhi Wang
{"title":"Stochastic Averaging Principle for Neutral Stochastic Functional Differential Equations Driven by G-Levy Process","authors":"Guangjun Shen, Jingjing Fan, Jiang-Lun Wu, Zhi Wang","doi":"10.1142/s0219493724500291","DOIUrl":"https://doi.org/10.1142/s0219493724500291","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141804355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantum Synchronization for Stochastic Schrodinger-Lohe Model 随机薛定谔-洛厄模型的量子同步
IF 0.8 4区 数学
Stochastics and Dynamics Pub Date : 2024-07-25 DOI: 10.1142/s0219493724500278
Li Lv, Zibo Wang, Jinqiao Duan
{"title":"Quantum Synchronization for Stochastic Schrodinger-Lohe Model","authors":"Li Lv, Zibo Wang, Jinqiao Duan","doi":"10.1142/s0219493724500278","DOIUrl":"https://doi.org/10.1142/s0219493724500278","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141803572","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Viability for Impulsive Stochastic Differential Inclusions Driven by Fractional Brownian Motion 分数布朗运动驱动的脉冲随机微分夹杂的可行性
IF 0.8 4区 数学
Stochastics and Dynamics Pub Date : 2024-07-12 DOI: 10.1142/s0219493724500266
N. N. Trong, Le Xuan Truong, T. Do
{"title":"Viability for Impulsive Stochastic Differential Inclusions Driven by Fractional Brownian Motion","authors":"N. N. Trong, Le Xuan Truong, T. Do","doi":"10.1142/s0219493724500266","DOIUrl":"https://doi.org/10.1142/s0219493724500266","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141655116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reflected stochastic differential equations driven by standard and fractional Brownian motion 标准和分数布朗运动驱动的反射随机微分方程
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-05-04 DOI: 10.1142/s0219493724500114
Monir Chadad, Mohamed Erraoui
{"title":"Reflected stochastic differential equations driven by standard and fractional Brownian motion","authors":"Monir Chadad, Mohamed Erraoui","doi":"10.1142/s0219493724500114","DOIUrl":"https://doi.org/10.1142/s0219493724500114","url":null,"abstract":"<p>The reflection problem on the positive half-line with reflection at zero for a time-dependent stochastic differential equations driven by standard and fractional Brownian motion with Hurst parameter <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>H</mi><mo>&gt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span><span></span> is considered. We prove the existence of weak solutions by using Euler scheme. Moreover, we show that pathwise uniqueness holds and a strong solution exists in the case of additive fractional noise and also up to a stopping time <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi></math></span><span></span> for the multiplicative case, but remains an open question beyond <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>τ</mi></math></span><span></span>.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimates of constants in the limit theorems for chaotic dynamical systems 混沌动力学系统极限定理中的常数估算
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-30 DOI: 10.1142/s0219493724500047
Leonid A. Bunimovich, Yaofeng Su
{"title":"Estimates of constants in the limit theorems for chaotic dynamical systems","authors":"Leonid A. Bunimovich, Yaofeng Su","doi":"10.1142/s0219493724500047","DOIUrl":"https://doi.org/10.1142/s0219493724500047","url":null,"abstract":"<p>In a vast area of probabilistic limit theorems for dynamical systems with chaotic behaviors always only functional form (exponential, power, etc.) of the asymptotic laws and of convergence rates were studied. However, for basically all applications, e.g., for computer simulations, development of algorithms to study chaotic dynamical systems numerically, as well as for design and analysis of real (e.g., in physics) experiments, the exact values (or at least estimates) of constants (parameters) of the functions, which appear in the asymptotic laws and rates of convergence, are of primary interest. In this paper, we provide such estimates of constants (parameters) in the central limit theorem, large deviations principle, law of large numbers and the rate of correlations decay for strongly chaotic dynamical systems.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Binary robustness of random attractors for 2D-Ginzburg–Landau equations with Wong–Zakai noise 具有 Wong-Zakai 噪声的二维金兹堡-兰道方程随机吸引子的二元鲁棒性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-30 DOI: 10.1142/s0219493724500102
Yangrong Li, Fengling Wang
{"title":"Binary robustness of random attractors for 2D-Ginzburg–Landau equations with Wong–Zakai noise","authors":"Yangrong Li, Fengling Wang","doi":"10.1142/s0219493724500102","DOIUrl":"https://doi.org/10.1142/s0219493724500102","url":null,"abstract":"<p>Consider a non-autonomous 2D-Ginzburg–Landau equation driven by Wong–Zakai noise or white noise, respectively, we first show the existence of pullback random attractors, which are random compact attracting sets indexed by two parameters: the size of Wong–Zakai noise and the current time. We then establish the robustness of the attractors when both parameters are simultaneously convergent. An essential difficulty arises from the possible loss of the convergence of solutions and only part convergence of solutions is available, which is a new phenomenon for 2D-GL equation distinguishing with the 1D case. So, by using <i>part</i> joint-convergence, regularity, eventual local-compactness and recurrence, we establish a binary robustness theorem of pullback random attractors and apply it to the weakly dissipative stochastic equation.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Averaging principle for stochastic 3D generalized Navier–Stokes equations 随机三维广义纳维-斯托克斯方程的平均原理
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-30 DOI: 10.1142/s0219493724500059
Hui Liu, Lin Lin, Yangyang Shi
{"title":"Averaging principle for stochastic 3D generalized Navier–Stokes equations","authors":"Hui Liu, Lin Lin, Yangyang Shi","doi":"10.1142/s0219493724500059","DOIUrl":"https://doi.org/10.1142/s0219493724500059","url":null,"abstract":"<p>In this paper, the multiscale stochastic 3D generalized Navier–Stokes equations are studied. By using Khasminkii’s time discretization approach and the technique of stopping time, the strong averaging principle for stochastic 3D generalized Navier–Stokes equations is proved in the space <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><msup><mrow><mi>ℍ</mi></mrow><mrow><mn>1</mn></mrow></msup><mo stretchy=\"false\">(</mo><msup><mrow><mi>𝕋</mi></mrow><mrow><mn>3</mn></mrow></msup><mo stretchy=\"false\">)</mo></math></span><span></span>.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reflected BSDEs driven by G-Brownian motion with time-varying Lipschitz coefficients 由具有时变 Lipschitz 系数的 G-Brownian 运动驱动的反射 BSDEs
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-30 DOI: 10.1142/s0219493724500072
Hanwu Li
{"title":"Reflected BSDEs driven by G-Brownian motion with time-varying Lipschitz coefficients","authors":"Hanwu Li","doi":"10.1142/s0219493724500072","DOIUrl":"https://doi.org/10.1142/s0219493724500072","url":null,"abstract":"<p>In this paper, we consider the reflected backward stochastic differential equations driven by <span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-Brownian motion (reflected <span><math altimg=\"eq-00003.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-BSDEs) with time-varying Lipschitz coefficients. We obtain the uniqueness result by establishing <i>a priori</i> estimates. For the existence, the solution can be approximated by a family of reflected <span><math altimg=\"eq-00004.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-BSDEs with Lipschitz conditions and by penalized <span><math altimg=\"eq-00005.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-BSDEs with time-varying coefficients. The latter approximation is useful to get the comparison theorem. Finally, we study the reflected <span><math altimg=\"eq-00006.gif\" display=\"inline\" overflow=\"scroll\"><mi>G</mi></math></span><span></span>-BSDEs with infinite time horizon.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827311","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamical behaviors of an impulsive stochastic neural field lattice model 脉冲随机神经场晶格模型的动力学行为
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-30 DOI: 10.1142/s0219493724500126
Tianhao Zeng, Shaoyue Mi, Dingshi Li
{"title":"Dynamical behaviors of an impulsive stochastic neural field lattice model","authors":"Tianhao Zeng, Shaoyue Mi, Dingshi Li","doi":"10.1142/s0219493724500126","DOIUrl":"https://doi.org/10.1142/s0219493724500126","url":null,"abstract":"<p>This paper is concerned with the asymptotic behaviors of the solutions of an impulsive stochastic neural field lattice model driven by nonlinear noise. We first show the existence and uniqueness of weak pullback mean random attractors for the impulsive stochastic systems. Then by the properties of Markov processes, the existence of evolution system of measures for the impulsive stochastic systems is established. To this end, we employ the idea of uniform estimates on the tails of the solutions to show the tightness of a family of distributions of the solutions of the lattice systems.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140827258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The fluctuational transition mechanism of non-hyperbolic chaotic invariant sets 非双曲混沌不变集的波动转换机制
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2024-04-25 DOI: 10.1142/s0219493724500163
Yicheng Mao, Xianbin Liu
{"title":"The fluctuational transition mechanism of non-hyperbolic chaotic invariant sets","authors":"Yicheng Mao, Xianbin Liu","doi":"10.1142/s0219493724500163","DOIUrl":"https://doi.org/10.1142/s0219493724500163","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140658510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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