Pub Date : 2024-03-01DOI: 10.1142/s0219493724500023
Wei Liu, Bin Pei, Qian Yu
{"title":"Rate of Convergence for the Smoluchowski-Kramers Approximation for Distribution Dependent SDEs Driven by Fractional Brownian Motions","authors":"Wei Liu, Bin Pei, Qian Yu","doi":"10.1142/s0219493724500023","DOIUrl":"https://doi.org/10.1142/s0219493724500023","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140089084","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 : 2024-03-01DOI: 10.1142/s0219493724500011
Badr Elmansouri, M. El Otmani
{"title":"Doubly Reflected BSDES Driven by RCLL Martingales Under Stochastic Lipschitz Coefficient","authors":"Badr Elmansouri, M. El Otmani","doi":"10.1142/s0219493724500011","DOIUrl":"https://doi.org/10.1142/s0219493724500011","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140087516","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 : 2023-12-01DOI: 10.1142/s0219493723500594
Zonghao Li, Jianhua Huang, Caibin Zeng
{"title":"Smoothness of invariant manifolds for stochastic evolution equations with non-dense domain","authors":"Zonghao Li, Jianhua Huang, Caibin Zeng","doi":"10.1142/s0219493723500594","DOIUrl":"https://doi.org/10.1142/s0219493723500594","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138620306","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 : 2023-11-10DOI: 10.1142/s0219493723500569
Andrey Dorogovtsev, Alexander Weib
The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically this can be characterised with the asymptotics of moments. In this article we show the existence of intermittency phenomena for SDEs with interaction with dissipative coefficients by showing uniform convergence of their Lyapunov exponents.
{"title":"Intermittency Phenomena for Mass Distributions of Stochastic Flows with Interaction","authors":"Andrey Dorogovtsev, Alexander Weib","doi":"10.1142/s0219493723500569","DOIUrl":"https://doi.org/10.1142/s0219493723500569","url":null,"abstract":"The intermittency phenomenon is the occurrence of very high but rare peaks, which despite their rarity influence the asymptotic behaviour of the underlying system. Mathematically this can be characterised with the asymptotics of moments. In this article we show the existence of intermittency phenomena for SDEs with interaction with dissipative coefficients by showing uniform convergence of their Lyapunov exponents.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186531","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 : 2023-11-10DOI: 10.1142/s0219493723500570
Po-Han Hsu, Padmanabhan Sundar
A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier-Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier-Stokes equation with Markov switching.
{"title":"Three-Dimensional stochastic Navier-Stokes equations with Markov switching","authors":"Po-Han Hsu, Padmanabhan Sundar","doi":"10.1142/s0219493723500570","DOIUrl":"https://doi.org/10.1142/s0219493723500570","url":null,"abstract":"A finite-state Markov chain is introduced in the noise terms of the three-dimensional stochastic Navier-Stokes equations in order to allow for transitions between two types of multiplicative noises. We call such systems as stochastic Navier-Stokes equations with Markov switching. To solve such a system, a family of regularized stochastic systems is introduced. For each such regularized system, the existence of a unique strong solution (in the sense of stochastic analysis) is established by the method of martingale problems and pathwise uniqueness. The regularization is removed in the limit by obtaining a weakly convergent sequence from the family of regularized solutions, and identifying the limit as a solution of the three-dimensional stochastic Navier-Stokes equation with Markov switching.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135186677","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 : 2023-11-08DOI: 10.1142/s0219493723400051
Lingyu Feng, Ting Gao, Ting Li, Zhongjie Lin, Xianming Liu
In this paper, we study a smooth approximation of an arbitrary càdlàg Lévy process. Such approximation processes are known as integrated fast oscillating Ornstein–Uhlenbeck (OU) processes. We know that approximating processes are continuous, while the limit of processes may be discontinuous, so convergence in uniform topology or Skorokhod [Formula: see text]-topology will not hold in general. Therefore, we establish an approximation in Skorokhod [Formula: see text]-topology. Note that the convergence is almost surely, which is an extension result of Hintze and Pavlyukevich.
{"title":"Approximations of Levy processes by integrated fast oscillating Ornstein-Uhlenbeck processes","authors":"Lingyu Feng, Ting Gao, Ting Li, Zhongjie Lin, Xianming Liu","doi":"10.1142/s0219493723400051","DOIUrl":"https://doi.org/10.1142/s0219493723400051","url":null,"abstract":"In this paper, we study a smooth approximation of an arbitrary càdlàg Lévy process. Such approximation processes are known as integrated fast oscillating Ornstein–Uhlenbeck (OU) processes. We know that approximating processes are continuous, while the limit of processes may be discontinuous, so convergence in uniform topology or Skorokhod [Formula: see text]-topology will not hold in general. Therefore, we establish an approximation in Skorokhod [Formula: see text]-topology. Note that the convergence is almost surely, which is an extension result of Hintze and Pavlyukevich.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135293378","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 : 2023-11-07DOI: 10.1142/s0219493723400038
Zhongyang Li, Fei Lu
In the inference for systems of interacting particles or agents, a coercivity condition ensures the identifiability of the interaction kernels, providing the foundation of learning. We prove the coercivity condition for stochastic systems with an arbitrary number of particles and a class of kernels such that the system of relative positions is ergodic. When the system of relative positions is stationary, we prove the coercivity condition by showing the strictly positive definiteness of an integral kernel arising in the learning. For the non-stationary case, we show that the coercivity condition holds when the time is large based on a perturbation argument.
{"title":"On the coercivity condition in the learning of interacting particle systems","authors":"Zhongyang Li, Fei Lu","doi":"10.1142/s0219493723400038","DOIUrl":"https://doi.org/10.1142/s0219493723400038","url":null,"abstract":"In the inference for systems of interacting particles or agents, a coercivity condition ensures the identifiability of the interaction kernels, providing the foundation of learning. We prove the coercivity condition for stochastic systems with an arbitrary number of particles and a class of kernels such that the system of relative positions is ergodic. When the system of relative positions is stationary, we prove the coercivity condition by showing the strictly positive definiteness of an integral kernel arising in the learning. For the non-stationary case, we show that the coercivity condition holds when the time is large based on a perturbation argument.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432015","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 : 2023-11-07DOI: 10.1142/s0219493723400063
Ting Li, Hongbo Fu, Xianming Liu
This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical [Formula: see text]-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as [Formula: see text]. Also, the rate of weak convergence, which depends on [Formula: see text], for the solution towards the solution of the limit equation is obtained. For illustration, the results are applied to a simple one-dimensional stochastic differential equation, which implies the rate of weak convergence is optimal.
{"title":"On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric α-stable Levy processes","authors":"Ting Li, Hongbo Fu, Xianming Liu","doi":"10.1142/s0219493723400063","DOIUrl":"https://doi.org/10.1142/s0219493723400063","url":null,"abstract":"This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical [Formula: see text]-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as [Formula: see text]. Also, the rate of weak convergence, which depends on [Formula: see text], for the solution towards the solution of the limit equation is obtained. For illustration, the results are applied to a simple one-dimensional stochastic differential equation, which implies the rate of weak convergence is optimal.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135432014","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 : 2023-11-03DOI: 10.1142/s021949372350051x
Ran Wang, Beibei Zhang
In this paper, we study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang [A. Matoussi, W. Sabbagh and T.-S. Zhang, Large deviation principles of obstacle problems for quasilinear stochastic PDEs, Appl. Math. Optim. 83(2) (2021) 849–879] plays an important role in the proof.
{"title":"A Large Deviation Principle for Reflected Spdes on Infinite Spatial Domain","authors":"Ran Wang, Beibei Zhang","doi":"10.1142/s021949372350051x","DOIUrl":"https://doi.org/10.1142/s021949372350051x","url":null,"abstract":"In this paper, we study a large deviation principle for a reflected stochastic partial differential equation on infinite spatial domain. A new sufficient condition for the weak convergence criterion proposed by Matoussi, Sabbagh and Zhang [A. Matoussi, W. Sabbagh and T.-S. Zhang, Large deviation principles of obstacle problems for quasilinear stochastic PDEs, Appl. Math. Optim. 83(2) (2021) 849–879] plays an important role in the proof.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775422","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 : 2023-11-03DOI: 10.1142/s021949372340004x
Xiujun Cheng, Wenzhuo Xiong, Huiru Wang
In this paper, we apply classical non-uniform L1 formula and the compact difference scheme for solving linear fractional systems with Neumann boundary conditions. A novelty and simple demonstration strategy is presented on the convergence analysis in the discrete maximum norm. Moreover, based on the special properties of the resulting coefficient matrix, diagonalization technique and discrete cosine transform (DCT) are adopted to speed up the convergence rate of the proposed method. In addition, the numerical scheme is also extended to the three-dimensional (3D) case. Several numerical experiments are given to support our findings.
{"title":"A Optimal Estimate for Linear Reaction Subdiffusion Equations with Neumann Boundary Conditions","authors":"Xiujun Cheng, Wenzhuo Xiong, Huiru Wang","doi":"10.1142/s021949372340004x","DOIUrl":"https://doi.org/10.1142/s021949372340004x","url":null,"abstract":"In this paper, we apply classical non-uniform L1 formula and the compact difference scheme for solving linear fractional systems with Neumann boundary conditions. A novelty and simple demonstration strategy is presented on the convergence analysis in the discrete maximum norm. Moreover, based on the special properties of the resulting coefficient matrix, diagonalization technique and discrete cosine transform (DCT) are adopted to speed up the convergence rate of the proposed method. In addition, the numerical scheme is also extended to the three-dimensional (3D) case. Several numerical experiments are given to support our findings.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775423","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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