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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":"28 1","pages":""},"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":"12 1","pages":""},"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":"80 1","pages":""},"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":"17 1","pages":""},"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":"13 1","pages":""},"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":"18 1","pages":""},"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
Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain 非密集域随机演化方程不变流形的平滑性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2023-12-01 DOI: 10.1142/s0219493723500594
Zonghao Li, Jianhua Huang, Caibin Zeng
{"title":"Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain","authors":"Zonghao Li, Jianhua Huang, Caibin Zeng","doi":"10.1142/s0219493723500594","DOIUrl":"https://doi.org/10.1142/s0219493723500594","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" 49","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138620306","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
Intermittency Phenomena for Mass Distributions of Stochastic Flows with Interaction 具有相互作用的随机流质量分布的间歇性现象
4区 数学
Stochastics and Dynamics Pub Date : 2023-11-10 DOI: 10.1142/s0219493723500569
Andrey Dorogovtsev, Alexander Weib
{"title":"Intermittency Phenomena for Mass Distributions of Stochastic Flows with Interaction","authors":"Andrey Dorogovtsev, Alexander Weib","doi":"10.1142/s0219493723500569","DOIUrl":"https://doi.org/10.1142/s0219493723500569","url":null,"abstract":"The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically this can be characterised with the asymptotics of moments. In this article we show the existence of intermittency phenomena for SDEs with interaction with dissipative coefficients by showing uniform convergence of their Lyapunov exponents.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" April","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186531","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
Three-Dimensional stochastic Navier-Stokes equations with Markov switching 具有马尔可夫转换的三维随机Navier-Stokes方程
4区 数学
Stochastics and Dynamics Pub Date : 2023-11-10 DOI: 10.1142/s0219493723500570
Po-Han Hsu, Padmanabhan Sundar
{"title":"Three-Dimensional stochastic Navier-Stokes equations with Markov switching","authors":"Po-Han Hsu, Padmanabhan Sundar","doi":"10.1142/s0219493723500570","DOIUrl":"https://doi.org/10.1142/s0219493723500570","url":null,"abstract":"A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier-Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier-Stokes equation with Markov switching.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" October","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186677","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: 1
Approximations of Levy processes by integrated fast oscillating Ornstein-Uhlenbeck processes 用积分快速振荡Ornstein-Uhlenbeck过程逼近Levy过程
4区 数学
Stochastics and Dynamics Pub Date : 2023-11-08 DOI: 10.1142/s0219493723400051
Lingyu Feng, Ting Gao, Ting Li, Zhongjie Lin, Xianming Liu
{"title":"Approximations of Levy processes by integrated fast oscillating Ornstein-Uhlenbeck processes","authors":"Lingyu Feng, Ting Gao, Ting Li, Zhongjie Lin, Xianming Liu","doi":"10.1142/s0219493723400051","DOIUrl":"https://doi.org/10.1142/s0219493723400051","url":null,"abstract":"In this paper, we study a smooth approximation of an arbitrary càdlàg Lévy process. Such approximation processes are known as integrated fast oscillating Ornstein–Uhlenbeck (OU) processes. We know that approximating processes are continuous, while the limit of processes may be discontinuous, so convergence in uniform topology or Skorokhod [Formula: see text]-topology will not hold in general. Therefore, we establish an approximation in Skorokhod [Formula: see text]-topology. Note that the convergence is almost surely, which is an extension result of Hintze and Pavlyukevich.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" 21","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293378","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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