Stochastics and Dynamics最新文献

{"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":"27 1","pages":"0"},"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}

{"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":"7 1","pages":"0"},"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}

{"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":" ","pages":""},"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}

{"title":"GAUSSIAN STRUCTURE IN COALESCING STOCHASTIC FLOWS","authors":"A. Dorogovtsev, K.V. Hlyniana","doi":"10.1142/s021949372350048x","DOIUrl":"https://doi.org/10.1142/s021949372350048x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48531190","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}

{"title":"Results on approximate controllability results for fractional stochastic delay differential systems of order r ∈ (1,2)","authors":"C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, K. Nisar, A. Shukla","doi":"10.1142/s0219493723500478","DOIUrl":"https://doi.org/10.1142/s0219493723500478","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41597042","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}

{"title":"Central Exponents of Linear Stochastic Differential Algebraic Equations of Index 1","authors":"Nguyen Thi The","doi":"10.1142/s0219493723500454","DOIUrl":"https://doi.org/10.1142/s0219493723500454","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49515086","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}

{"title":"Quadratic BSDEs with mean reflection driven by G-Brownian motion","authors":"Zihao Gu, Yiqing Lin, Kun Xu","doi":"10.1142/s0219493723500442","DOIUrl":"https://doi.org/10.1142/s0219493723500442","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44031073","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}

{"title":"Stochastic newton equations in the strong potential limit for the multi-dimensional case","authors":"Song Liang","doi":"10.1142/s0219493723500430","DOIUrl":"https://doi.org/10.1142/s0219493723500430","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48246753","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}

{"title":"The asymptotic behaviour of solutions for stochastic evolution equations with pantograph delay","authors":"Yarong Liu, Yejuan Wang, T. Caraballo","doi":"10.1142/s0219493723500429","DOIUrl":"https://doi.org/10.1142/s0219493723500429","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43286021","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}

{"title":"Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model","authors":"Dan Crisan, Darryl D. Holm, Oana Lang, Prince Romeo Mensah, Wei Pan","doi":"10.1142/s0219493723500399","DOIUrl":"https://doi.org/10.1142/s0219493723500399","url":null,"abstract":"<p>This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrization of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect the dynamics, particularly at the submesoscale (250<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>m–10<span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mspace width=\".17em\"></mspace></math></span><span></span>km). Specifically, we have chosen the Stochastic Advection by Lie Transport (SALT) algorithm introduced in [D. D. Holm, Variational principles for stochastic fluid dynamics, <i>Proc. Roy. Soc. A: Math. Phys. Eng. Sci.</i><b>471</b> (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963] and applied in [C. Cotter, D. Crisan, D. Holm, W. Pan and I. Shevchenko, Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model, <i>Found. Data Sci.</i><b>2</b> (2020) 173, https://doi.org/10.3934/fods.2020010; Numerically modeling stochastic lie transport in fluid dynamics, <i>SIAM Multiscale Model. Simul.</i><b>17</b> (2019) 192–232, https://doi.org/10.1137/18M1167929] as our modeling approach. The SALT approach preserves the Kelvin circulation theorem and an infinite family of integral conservation laws for TQG. The goal of the SALT algorithm is to quantify the uncertainty in the process of up-scaling, or coarse-graining of either observed or synthetic data at fine scales, for use in computational simulations at coarser scales. The present work provides a rigorous mathematical analysis of the solution properties of the thermal quasigeostrophic (TQG) equations with SALT [D. D. Holm and E. Luesink, Stochastic wave-current interaction in thermal shallow water dynamics, <i>J. Nonlinear Sci.</i><b>31</b> (2021), https://doi.org/10.1007/s00332-021-09682-9; D. D. Holm, E. Luesink and W. Pan, Stochastic mesoscale circulation dynamics in the thermal ocean, <i>Phys. Fluids</i><b>33</b> (2021) 046603, https://doi.org/10.1063/5.0040026].</p>","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":"128 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138508010","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}