Pub Date : 2022-11-09DOI: 10.1142/s0219493722400317
G. Lv, Jinlong Wei
{"title":"The probability of events for stochastic parabolic equations","authors":"G. Lv, Jinlong Wei","doi":"10.1142/s0219493722400317","DOIUrl":"https://doi.org/10.1142/s0219493722400317","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47104695","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 : 2022-10-28DOI: 10.1142/s0219493722400275
Yueyang Wang, Guanggan Chen, Min Yang
This work is concerned with a stochastic Leray-[Formula: see text] system with fractional dissipation driven by multiplicative noise. It establishes the central limit theorem of the stochastic system. Moreover, building a new auxiliary system and using the classical weak convergence approach, it derives the moderate deviation principle of the stochastic system.
{"title":"Deviation principles of a stochastic leray-α system with fractional dissipation","authors":"Yueyang Wang, Guanggan Chen, Min Yang","doi":"10.1142/s0219493722400275","DOIUrl":"https://doi.org/10.1142/s0219493722400275","url":null,"abstract":"This work is concerned with a stochastic Leray-[Formula: see text] system with fractional dissipation driven by multiplicative noise. It establishes the central limit theorem of the stochastic system. Moreover, building a new auxiliary system and using the classical weak convergence approach, it derives the moderate deviation principle of the stochastic system.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46471081","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 : 2022-10-15DOI: 10.1142/s0219493723500089
Yukihiro Tsuzuki
{"title":"Some Perpetual Integral Functionals of the Three-Dimensional Bessel Process","authors":"Yukihiro Tsuzuki","doi":"10.1142/s0219493723500089","DOIUrl":"https://doi.org/10.1142/s0219493723500089","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42915931","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 : 2022-09-27DOI: 10.1142/s0219493723500387
V. Vargas
Let $M$ be a compact metric space and $X = M^{mathbb{N}}$, we consider a set of admissible sequences $X_{A, I} subset X$ determined by a continuous admissibility function $A : M times M to mathbb{R}$ and a compact set $I subset mathbb{R}$. Given a Lipschitz continuous potential $varphi : X_{A, I} to mathbb{R}$, we prove uniqueness of the Gibbs state $mu_varphi$ and we show that it is a Gibbs-Bowen measure and satisfies a central limit theorem.
设$M$为紧度量空间$X = M^{mathbb{N}}$，考虑由连续容许函数$A : M times M to mathbb{R}$和紧集$I subset mathbb{R}$确定的容许序列集$X_{A, I} subset X$。给定一个Lipschitz连续势$varphi : X_{A, I} to mathbb{R}$，我们证明了Gibbs态的唯一性$mu_varphi$，并证明了它是Gibbs- bowen测度，满足中心极限定理。
{"title":"Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattices with markovian structure","authors":"V. Vargas","doi":"10.1142/s0219493723500387","DOIUrl":"https://doi.org/10.1142/s0219493723500387","url":null,"abstract":"Let $M$ be a compact metric space and $X = M^{mathbb{N}}$, we consider a set of admissible sequences $X_{A, I} subset X$ determined by a continuous admissibility function $A : M times M to mathbb{R}$ and a compact set $I subset mathbb{R}$. Given a Lipschitz continuous potential $varphi : X_{A, I} to mathbb{R}$, we prove uniqueness of the Gibbs state $mu_varphi$ and we show that it is a Gibbs-Bowen measure and satisfies a central limit theorem.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48517839","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 : 2022-08-13DOI: 10.1142/s021949372240038x
Xianjin Cheng, Zhenxin Liu, Lixin Zhang
. In this paper, we study the existence of n -dimensional linear stochastic differential equations (SDEs) such that the sign of Lyapunov exponents are changed under an exponentially decaying perturbation. First, we show that the equation with all positive Lyapunov exponents will have n − 1 linearly independent solutions with negative Lyapunov exponents under the perturbation. Meanwhile, we prove that the equation with all negative Lyapunov exponents will also have solutions with positive Lyapunov exponents under another similar perturbation. Finally, we also show that other three kinds of perturbations which appear at different positions of the equation will change the sign of Lyapunov exponents.
{"title":"Small perturbations may change the sign of Lyapunov exponents for linear SDEs","authors":"Xianjin Cheng, Zhenxin Liu, Lixin Zhang","doi":"10.1142/s021949372240038x","DOIUrl":"https://doi.org/10.1142/s021949372240038x","url":null,"abstract":". In this paper, we study the existence of n -dimensional linear stochastic differential equations (SDEs) such that the sign of Lyapunov exponents are changed under an exponentially decaying perturbation. First, we show that the equation with all positive Lyapunov exponents will have n − 1 linearly independent solutions with negative Lyapunov exponents under the perturbation. Meanwhile, we prove that the equation with all negative Lyapunov exponents will also have solutions with positive Lyapunov exponents under another similar perturbation. Finally, we also show that other three kinds of perturbations which appear at different positions of the equation will change the sign of Lyapunov exponents.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48163210","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 : 2022-08-10DOI: 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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
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