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Stochastics and Dynamics最新文献

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Convergence problem of reduced Ostrovsky equation in Fourier-Lebesgue spaces with rough data and random data 具有粗糙数据和随机数据的傅立叶-勒贝格空间中简化Ostrovsky方程的收敛性问题
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-06-03 DOI: 10.1142/s0219493723500016
Xiangqian Yan, Wei Yan, Yajuan Zhao, Meihua Yang
{"title":"Convergence problem of reduced Ostrovsky equation in Fourier-Lebesgue spaces with rough data and random data","authors":"Xiangqian Yan, Wei Yan, Yajuan Zhao, Meihua Yang","doi":"10.1142/s0219493723500016","DOIUrl":"https://doi.org/10.1142/s0219493723500016","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41843953","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
Deviation properties for linear self-attracting diffusion process and applications 线性自吸引扩散过程的偏差特性及其应用
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-06-03 DOI: 10.1142/s0219493722500289
Hui Jiang, Yajuan Pan
{"title":"Deviation properties for linear self-attracting diffusion process and applications","authors":"Hui Jiang, Yajuan Pan","doi":"10.1142/s0219493722500289","DOIUrl":"https://doi.org/10.1142/s0219493722500289","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44742653","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
Periodic measures for a class of SPDEs with regime-switching 一类带状态交换的spde的周期测度
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-06-02 DOI: 10.1142/s021949372350034x
Chun Ho Lau, Weiling Sun
{"title":"Periodic measures for a class of SPDEs with regime-switching","authors":"Chun Ho Lau, Weiling Sun","doi":"10.1142/s021949372350034x","DOIUrl":"https://doi.org/10.1142/s021949372350034x","url":null,"abstract":"We use the variational approach to investigate periodic measures for a class of SPDEs with regime-switching. The hybrid system is driven by degenerate L'{e}vy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the associated time-inhomogeneous semigroup. The main results are applied to stochastic porous media equations with regime-switching.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45479125","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
Random attractors for setvalued dynamical systems for stochastic evolution equations driven by a nontrivial fractional noise 非平凡分数噪声驱动随机演化方程集值动力系统的随机吸引子
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-05-14 DOI: 10.1142/s0219493722400184
M. Garrido-Atienza, B. Schmalfuss, J. Valero
{"title":"Random attractors for setvalued dynamical systems for stochastic evolution equations driven by a nontrivial fractional noise","authors":"M. Garrido-Atienza, B. Schmalfuss, J. Valero","doi":"10.1142/s0219493722400184","DOIUrl":"https://doi.org/10.1142/s0219493722400184","url":null,"abstract":"We consider a stochastic evolution equation driven by a fractional Brownian motion in a separable Hilbert space with Hurst parameter [Formula: see text]. The coefficient in front of the noise is in general nonlinear. The related integral is a pathwise integral defined by fractional derivatives. The nonlinear coefficients of this equation satisfy weak conditions ensuring only existence of a solution but not uniqueness. This equation generates then a multivalued random dynamical system. We prove the existence of a random attractor for this system.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43206107","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: 2
Invariant measures and boundedness in the mean for stochastic equations driven by Lévy noise 由lsamvy噪声驱动的随机方程的均值的不变测度和有界性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-05-14 DOI: 10.1142/s0219493722400196
B. Maslowski, O. Týbl
{"title":"Invariant measures and boundedness in the mean for stochastic equations driven by Lévy noise","authors":"B. Maslowski, O. Týbl","doi":"10.1142/s0219493722400196","DOIUrl":"https://doi.org/10.1142/s0219493722400196","url":null,"abstract":"Existence of invariant measures and average stability in the mean are studied for stochastic differential equations driven by Lévy process. In particular, some natural conditions are found that verify stabilization of the equation (in the sense of the existence of invariant measures) by jump noise terms. These conditions are verified in several examples.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41439752","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
Local zero-stability of rough evolution equations 粗糙演化方程的局部零稳定性
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-05-10 DOI: 10.1142/s0219493722400159
R. Hesse
{"title":"Local zero-stability of rough evolution equations","authors":"R. Hesse","doi":"10.1142/s0219493722400159","DOIUrl":"https://doi.org/10.1142/s0219493722400159","url":null,"abstract":"We analyze the long time behavior of solutions to rough parabolic equations. More precisely, we show local exponential stability for the mild solution driven by a fractional Brownian motion with Hurst parameter [Formula: see text].","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46219334","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
Typical Properties of Ergodic Optimization for Asymptotically Additive Potentials 渐近可加势遍历优化的典型性质
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-05-04 DOI: 10.1142/s0219493722500241
T. Bomfim, R. Huo, P. Varandas, Y. Zhao
{"title":"Typical Properties of Ergodic Optimization for Asymptotically Additive Potentials","authors":"T. Bomfim, R. Huo, P. Varandas, Y. Zhao","doi":"10.1142/s0219493722500241","DOIUrl":"https://doi.org/10.1142/s0219493722500241","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42884213","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: 3
Quadratic variation and drift parameter estimation for the stochastic wave equation with space-time white noise 时空白噪声随机波动方程的二次变分及漂移参数估计
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-04-29 DOI: 10.1142/s0219493722400147
Obayda Assaad, Julie Gamain, C. Tudor
{"title":"Quadratic variation and drift parameter estimation for the stochastic wave equation with space-time white noise","authors":"Obayda Assaad, Julie Gamain, C. Tudor","doi":"10.1142/s0219493722400147","DOIUrl":"https://doi.org/10.1142/s0219493722400147","url":null,"abstract":"We study the quadratic variations (in time and in space) of the solution to the stochastic wave equation driven by the space-time white noise. We give their limit (almost surely and in [Formula: see text]) and we prove that these variations satisfy, after a proper renormalization, a Central Limit Theorem. We apply the quadratic variation to define and analyze estimators for the drift parameter of the wave equation.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46587586","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
Singular limits for stochastic equations 随机方程的奇异极限
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-04-20 DOI: 10.1142/S0219493723500405
D. Blomker, Jonas M. Tolle
{"title":"Singular limits for stochastic equations","authors":"D. Blomker, Jonas M. Tolle","doi":"10.1142/S0219493723500405","DOIUrl":"https://doi.org/10.1142/S0219493723500405","url":null,"abstract":"We study singular limits of stochastic evolution equations in the interplay of disappearing strength of the noise and insufficient regularity, where the equation in the limit with noise would not be defined due to lack of regularity. We recover previously known results on vanishing small noise with increasing roughness, but our main focus is to study for fixed noise the singular limit where the leading order differential operator in the equation may vanish. Although the noise is disappearing in the limit, additional deterministic terms appear due to renormalization effects. We separate the analysis of the equation from the convergence of stochastic terms and give a general framework for the main error estimates. This first reduces the result to bounds on a residual and in a second step to various bounds on the stochastic convolution. Moreover, as examples we apply our result to the a singularly regularized Allen-Cahn equation with a vanishing Bilaplacian, and the Cahn-Hilliard/Allen-Cahn homotopy with space-time white noise in two spatial dimensions.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45757629","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
Stochastic elliptic-parabolic system arising in porous media 多孔介质中出现的随机椭圆-抛物系统
IF 1.1 4区 数学
Stochastics and Dynamics Pub Date : 2022-04-18 DOI: 10.1142/s0219493722400226
H. Bessaih, Cynthia Cohn, O. Landoulsi
{"title":"Stochastic elliptic-parabolic system arising in porous media","authors":"H. Bessaih, Cynthia Cohn, O. Landoulsi","doi":"10.1142/s0219493722400226","DOIUrl":"https://doi.org/10.1142/s0219493722400226","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49186651","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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