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Stochastics and Dynamics最新文献

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Stochastic rotating waves 随机旋转波
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-19 DOI: 10.1142/s0219493722400299
Christian Kuehn, James MacLaurin, Giulio Zucal
{"title":"Stochastic rotating waves","authors":"Christian Kuehn, James MacLaurin, Giulio Zucal","doi":"10.1142/s0219493722400299","DOIUrl":"https://doi.org/10.1142/s0219493722400299","url":null,"abstract":"<p>Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has recently received considerable attention are traveling wave patterns occurring in stochastic partial differential equations (SPDEs). Here, one is interested in how deterministic traveling waves behave under stochastic perturbations. In this paper, we start the mathematical study of a related class of problems: stochastic rotating waves generated by SPDEs. We combine deterministic partial differential equation (PDE) dynamics techniques with methods from stochastic analysis. We establish two different approaches, the variational phase and the approximated variational phase, for defining stochastic phase variables along the rotating wave, which track the effect of noise on neutral spectral modes associated to the special Euclidean symmetry group of rotating waves. Furthermore, we prove transverse stability results for rotating waves showing that over certain time scales and for small noise, the stochastic rotating wave stays close to its deterministic counterpart.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531952","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
Approximation for a generalized Langevin equation with high oscillation in time and space 具有高时空振荡的广义朗之万方程的近似
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-13 DOI: 10.1142/s0219493722400305
Dong Su, Wei Wang
{"title":"Approximation for a generalized Langevin equation with high oscillation in time and space","authors":"Dong Su, Wei Wang","doi":"10.1142/s0219493722400305","DOIUrl":"https://doi.org/10.1142/s0219493722400305","url":null,"abstract":"<p>This paper derives an approximation for a generalized Langevin equation driven by a force with random oscillation in time and periodic oscillation in space. By a diffusion approximation and the weak convergence of periodic oscillation function, the solution of the generalized Langevin equation is shown to converge in distribution to the solution of a stochastic partial differential equations (SPDEs) driven by time white noise.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531949","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
Bohl–Perron theorem for random dynamical systems 随机动力系统的Bohl-Perron定理
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-13 DOI: 10.1142/s0219493723500107
Nguyen Huu Du, Tran Manh Cuong, Ta Thi Trang
{"title":"Bohl–Perron theorem for random dynamical systems","authors":"Nguyen Huu Du, Tran Manh Cuong, Ta Thi Trang","doi":"10.1142/s0219493723500107","DOIUrl":"https://doi.org/10.1142/s0219493723500107","url":null,"abstract":"<p>In this paper, we consider the Bohl–Perron Theorem for linear random dynamical systems. We prove that the tempered exponential stability of a linear co-cycle is equivalent to the boundedness of solutions for inherit difference equation. Paper also proves a similar concept for co-cycle admitting a tempered exponential dichotomy.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531950","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
Convergence of nonlinear filtering for multiscale systems with correlated Levy noises 具有相关Levy噪声的多尺度系统非线性滤波的收敛性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-07 DOI: 10.1142/s0219493723500168
H. Qiao
{"title":"Convergence of nonlinear filtering for multiscale systems with correlated Levy noises","authors":"H. Qiao","doi":"10.1142/s0219493723500168","DOIUrl":"https://doi.org/10.1142/s0219493723500168","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42736258","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
An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion 次分数布朗运动下模糊随机微分方程的近似方法
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-07 DOI: 10.1142/s021949372350017x
H. Jafari, Hamed Farahani, M. J. Ebadi
{"title":"An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion","authors":"H. Jafari, Hamed Farahani, M. J. Ebadi","doi":"10.1142/s021949372350017x","DOIUrl":"https://doi.org/10.1142/s021949372350017x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42694894","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
Dynamics of a multi-species lottery competition model in stochastic environments 随机环境下多物种彩票竞争模型的动力学
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-06 DOI: 10.1142/s0219493722400287
Jiaqi Cheng, Xiaoying Han, Ming Liao
{"title":"Dynamics of a multi-species lottery competition model in stochastic environments","authors":"Jiaqi Cheng, Xiaoying Han, Ming Liao","doi":"10.1142/s0219493722400287","DOIUrl":"https://doi.org/10.1142/s0219493722400287","url":null,"abstract":"<p>An <i>N</i>-dimensional lottery model for competition among <span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>N</mi><mo>≥</mo><mn>2</mn></math></span><span></span> ecological species in stochastic environments is studied under the i.i.d. assumption. First, a system of nonlinear stochastic differential equations (SDEs) is developed as the diffusion approximation for the discrete lottery model. Then the existence and uniqueness of positive and bounded global solutions, as well as long-term dynamics for the solution are investigated. In particular, sufficient conditions under which extinction and persistence occur are constructed, respectively.</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138531948","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
A two-dimensional stochastic fractional non-local diffusion lattice model with delays 具有时滞的二维随机分数阶非局部扩散格模型
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-12-01 DOI: 10.1142/s0219493722400329
Yejuan Wang, Yu Wang, Xiaoying Han, P. Kloeden
{"title":"A two-dimensional stochastic fractional non-local diffusion lattice model with delays","authors":"Yejuan Wang, Yu Wang, Xiaoying Han, P. Kloeden","doi":"10.1142/s0219493722400329","DOIUrl":"https://doi.org/10.1142/s0219493722400329","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46138670","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
Preface for the Second Volume of the Special Issue Dedicated to the 65th Birthday of Björn Schmalfuß 纪念比约恩·施马尔夫65岁诞辰特刊第二卷序言
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-11-29 DOI: 10.1142/s0219493722020038
Alexandra Neam, Jinqiao Duan
{"title":"Preface for the Second Volume of the Special Issue Dedicated to the 65th Birthday of Björn Schmalfuß","authors":"Alexandra Neam, Jinqiao Duan","doi":"10.1142/s0219493722020038","DOIUrl":"https://doi.org/10.1142/s0219493722020038","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44094630","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 exponential behavior and stability of the stochastic three-dimensional primitive equations driven by Lévy noise Lévy噪声驱动的随机三维原始方程的指数行为及其稳定性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-11-12 DOI: 10.1142/s0219493723500077
Dong Su, Hui Liu
{"title":"The exponential behavior and stability of the stochastic three-dimensional primitive equations driven by Lévy noise","authors":"Dong Su, Hui Liu","doi":"10.1142/s0219493723500077","DOIUrl":"https://doi.org/10.1142/s0219493723500077","url":null,"abstract":"This paper establishes the exponential behavior and stability of the stochastic three-dimensional primitive equations driven by Lévy noise via Burkholder–Davis–Gundy inequality and Itô formula. In particular, we prove that under some conditions on the forcing terms, the weak solution converges exponentially in the mean square and almost surely exponentially to the stationary solution.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44327304","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
On the rate of convergence of weighted oscillating ergodic averages 加权振荡遍历平均的收敛速度
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-11-11 DOI: 10.1142/s0219493723500144
A. Darwiche, Dominique Schneider
{"title":"On the rate of convergence of weighted oscillating ergodic averages","authors":"A. Darwiche, Dominique Schneider","doi":"10.1142/s0219493723500144","DOIUrl":"https://doi.org/10.1142/s0219493723500144","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43033978","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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