Pub Date : 2022-06-03DOI: 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}
Pub Date : 2022-06-03DOI: 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}
Pub Date : 2022-06-02DOI: 10.1142/s021949372350034x
Chun Ho Lau, Weiling Sun
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.
{"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}
Pub Date : 2022-05-14DOI: 10.1142/s0219493722400184
M. Garrido-Atienza, B. Schmalfuss, J. Valero
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.
{"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}
Pub Date : 2022-05-14DOI: 10.1142/s0219493722400196
B. Maslowski, O. Týbl
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.
{"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}
Pub Date : 2022-05-10DOI: 10.1142/s0219493722400159
R. Hesse
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].
{"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}
Pub Date : 2022-05-04DOI: 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}
Pub Date : 2022-04-29DOI: 10.1142/s0219493722400147
Obayda Assaad, Julie Gamain, C. Tudor
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.
{"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}
Pub Date : 2022-04-20DOI: 10.1142/S0219493723500405
D. Blomker, Jonas M. Tolle
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.
{"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}
Pub Date : 2022-04-18DOI: 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}
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