Pub Date : 2022-08-10DOI: 10.1142/s0219493722500307
Kexiang Yang, Ercai Chen, Xiaoyao Zhou
{"title":"On the Induced Measure-Theoretic Entropy for Random Dynamical Systems","authors":"Kexiang Yang, Ercai Chen, Xiaoyao Zhou","doi":"10.1142/s0219493722500307","DOIUrl":"https://doi.org/10.1142/s0219493722500307","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45413783","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 : 2022-07-22DOI: 10.1142/s0219493723500053
J. Garzón, J. León, S. Torres
{"title":"Representation of solutions to sticky stochastic differential equations","authors":"J. Garzón, J. León, S. Torres","doi":"10.1142/s0219493723500053","DOIUrl":"https://doi.org/10.1142/s0219493723500053","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46707982","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 : 2022-06-17DOI: 10.1142/s021949372350003x
Junfeng Liu, Zhi Wang, Zengwu Wang
{"title":"Space-time fractional Anderson model driven by Gaussian noise rough in space","authors":"Junfeng Liu, Zhi Wang, Zengwu Wang","doi":"10.1142/s021949372350003x","DOIUrl":"https://doi.org/10.1142/s021949372350003x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41424534","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 : 2022-06-17DOI: 10.1142/s0219493723500041
M. Kiyanpour, B. Z. Zangeneh, Ruhollah Jahanipur
{"title":"Global solution to non self-adjoint stochastic Volterra Equation","authors":"M. Kiyanpour, B. Z. Zangeneh, Ruhollah Jahanipur","doi":"10.1142/s0219493723500041","DOIUrl":"https://doi.org/10.1142/s0219493723500041","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46992952","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/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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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":" ","pages":""},"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}
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