Pub Date : 2023-10-27DOI: 10.1142/s0219493723500557
Jinlong Wei, Guangying Lv
{"title":"The Impact of noise on Burgers equations","authors":"Jinlong Wei, Guangying Lv","doi":"10.1142/s0219493723500557","DOIUrl":"https://doi.org/10.1142/s0219493723500557","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136312425","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 : 2023-10-06DOI: 10.1142/s0219493723400026
Ting Gao, Jinqiao Duan
{"title":"Stochastic Dynamics and Data Science","authors":"Ting Gao, Jinqiao Duan","doi":"10.1142/s0219493723400026","DOIUrl":"https://doi.org/10.1142/s0219493723400026","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350366","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 : 2023-10-06DOI: 10.1142/s0219493723400087
Wei Wei, Jianyu Hu, Jinqiao Duan
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, we find that the rate function (or action functional) does not involve with the solution of the skeleton equation, which describes unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution-dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.
{"title":"The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems","authors":"Wei Wei, Jianyu Hu, Jinqiao Duan","doi":"10.1142/s0219493723400087","DOIUrl":"https://doi.org/10.1142/s0219493723400087","url":null,"abstract":"Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, we find that the rate function (or action functional) does not involve with the solution of the skeleton equation, which describes unperturbed deterministic flow of the vector field shifted by the interaction at zero distance. As a result, we are led to study the most likely transition path for a stochastic differential equation without distribution-dependency. This enables the computation of the most likely transition path for these distribution-dependent stochastic dynamical systems by the adaptive minimum action method and we illustrate our approach in two examples.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302005","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 : 2023-10-06DOI: 10.1142/s0219493723400105
Jian Ren, Jinqiao Duan
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data of the most probable transition trajectory. By the Onsager-Machlup theory, the most probable transition trajectory satisfies the corresponding Euler-Lagrange equation, which is a second order deterministic ordinary differential equation involving the drift term and diffusion coefficient. We first estimate the coefficients of the Euler-Lagrange equation based on the data of the most probable trajectory, and then we calculate the drift and diffusion coefficients of the governing stochastic dynamical system. These two steps involve sparse regression and optimization. Finally, we illustrate our method with an example and some discussions.
{"title":"Identifying stochastic governing equations from data of the most probable transition trajectories","authors":"Jian Ren, Jinqiao Duan","doi":"10.1142/s0219493723400105","DOIUrl":"https://doi.org/10.1142/s0219493723400105","url":null,"abstract":"Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data of the most probable transition trajectory. By the Onsager-Machlup theory, the most probable transition trajectory satisfies the corresponding Euler-Lagrange equation, which is a second order deterministic ordinary differential equation involving the drift term and diffusion coefficient. We first estimate the coefficients of the Euler-Lagrange equation based on the data of the most probable trajectory, and then we calculate the drift and diffusion coefficients of the governing stochastic dynamical system. These two steps involve sparse regression and optimization. Finally, we illustrate our method with an example and some discussions.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302734","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 : 2023-10-06DOI: 10.1142/s0219493723400099
Yi Wang, Qing Guo, Min Zhao, Chuanjun Dai, He Liu
{"title":"Dynamics of a Stochastic Phytoplankton-Zooplankton System with Defensive and Offensive Effects","authors":"Yi Wang, Qing Guo, Min Zhao, Chuanjun Dai, He Liu","doi":"10.1142/s0219493723400099","DOIUrl":"https://doi.org/10.1142/s0219493723400099","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350536","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 : 2023-10-06DOI: 10.1142/s0219493723500521
Anatolii A. Puhalskii
This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function possesses certain structure and the invariant measures are exponentially tight, then the LDP for the invariant measures is implied by the sample path LDP, no other properties of the stochastic processes in question being material. As an application, we obtain an LDP for the stationary distributions of jump diffusions. Methods of large deviation convergence and idempotent probability play an integral part.
{"title":"Large deviation limits of invariant measures","authors":"Anatolii A. Puhalskii","doi":"10.1142/s0219493723500521","DOIUrl":"https://doi.org/10.1142/s0219493723500521","url":null,"abstract":"This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function possesses certain structure and the invariant measures are exponentially tight, then the LDP for the invariant measures is implied by the sample path LDP, no other properties of the stochastic processes in question being material. As an application, we obtain an LDP for the stationary distributions of jump diffusions. Methods of large deviation convergence and idempotent probability play an integral part.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135302593","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 : 2023-10-06DOI: 10.1142/s0219493723400075
Linghongzhi Lu, Yang Li, Xianbin Liu
{"title":"Data-driven method to extract mean exit time and escape probability for dynamical systems driven by Levy noises","authors":"Linghongzhi Lu, Yang Li, Xianbin Liu","doi":"10.1142/s0219493723400075","DOIUrl":"https://doi.org/10.1142/s0219493723400075","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135350517","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 : 2023-09-01DOI: 10.1142/s0219493723500491
Bixiang Wang
{"title":"Uniform large deviations of fractional stochastic equations with polynomial drift on unbounded domains","authors":"Bixiang Wang","doi":"10.1142/s0219493723500491","DOIUrl":"https://doi.org/10.1142/s0219493723500491","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43456698","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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