Pub Date : 2023-09-01DOI: 10.1142/s0219493723500478
C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, K. Nisar, A. Shukla
{"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":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":"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}
Pub Date : 2023-08-10DOI: 10.1142/s0219493723500454
Nguyen Thi The
{"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":null,"pages":null},"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}
Pub Date : 2023-07-14DOI: 10.1142/s0219493723500430
Song Liang
{"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":null,"pages":null},"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}
Pub Date : 2023-07-14DOI: 10.1142/s0219493723500442
Zihao Gu, Yiqing Lin, Kun Xu
{"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":null,"pages":null},"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}
Pub Date : 2023-07-14DOI: 10.1142/s0219493723500429
Yarong Liu, Yejuan Wang, T. Caraballo
{"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":null,"pages":null},"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}
Pub Date : 2023-07-05DOI: 10.1142/s0219493723500399
Dan Crisan, Darryl D. Holm, Oana Lang, Prince Romeo Mensah, Wei Pan
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 (250m–10km). Specifically, we have chosen the Stochastic Advection by Lie Transport (SALT) algorithm introduced in [D. D. Holm, Variational principles for stochastic fluid dynamics, Proc. Roy. Soc. A: Math. Phys. Eng. Sci.471 (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, Found. Data Sci.2 (2020) 173, https://doi.org/10.3934/fods.2020010; Numerically modeling stochastic lie transport in fluid dynamics, SIAM Multiscale Model. Simul.17 (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, J. Nonlinear Sci.31 (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, Phys. Fluids33 (2021) 046603, https://doi.org/10.1063/5.0040026].
本文研究了位涡动力学平衡二维热准地转(TQG)随机模型的数学性质。当水平浮力梯度和水深测量影响上层海洋动力学时，特别是在亚中尺度(250m-10km)，该随机TQG模型旨在作为上层海洋动力学计算模拟中未解决自由度动力学参数化的基础。具体而言，我们选择了[D]中介绍的随机平流by Lie Transport (SALT)算法。D. Holm，随机流体动力学的变分原理，罗伊出版社。Soc。答:数学。理论物理。Eng。Sci.471 (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963]，并应用于[C]。Cotter, D. Crisan, D. Holm, W. Pan和I. Shevchenko，在2层准地转模型中使用随机输运噪声建模不确定性，发现。数据科学2 (2020)173,https://doi.org/10.3934/fods.2020010;流体动力学中随机lie输运的数值模拟，SIAM多尺度模型。Simul.17 (2019) 192-232, https://doi.org/10.1137/18M1167929]作为我们的建模方法。SALT方法保留了开尔文循环定理和TQG的无穷一族积分守恒定律。SALT算法的目标是量化放大过程中的不确定性，或者在精细尺度上对观测数据或合成数据进行粗粒度处理，以便在更大尺度上进行计算模拟。本文对含SALT的热准地转(TQG)方程的解性质进行了严格的数学分析[D]。D. Holm和E. Luesink，热浅水动力学随机波流相互作用[j] .非线性科学31 (2021)，https://doi.org/10.1007/s00332-021-09682-9;黄晓明，黄晓明，黄晓明，热海洋随机中尺度环流动力学，物理学报。流体学报，33 (2021)046603,https://doi.org/10.1063/5.0040026]。
{"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":null,"pages":null},"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}
Pub Date : 2023-05-17DOI: 10.1142/s0219493723500508
R. Balan, X. Liang
In this article, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is interpreted in the Skorohod sense, using Malliavin calculus. We consider two cases: (i) the regular noise, whose spatial covariance is given by the Riesz kernel of order $alpha in (0,d)$, in spatial dimension $dgeq 1$; (ii) the rough noise, which is fractional in space with Hurst index $H<1/2$, in spatial dimension $d=1$. We assume that the noise is colored in time. The similar problem for the white noise in time was considered in Bezdek (2016) and Giordano, Jolis and Quer-Sardanyons (2020).
{"title":"Continuity in law for solutions of SPDEs with space-time homogeneous Gaussian noise","authors":"R. Balan, X. Liang","doi":"10.1142/s0219493723500508","DOIUrl":"https://doi.org/10.1142/s0219493723500508","url":null,"abstract":"In this article, we study the continuity in law of the solutions of two linear multiplicative SPDEs (the parabolic Anderson model and the hyperbolic Anderson model) with respect to the spatial parameter of the noise. The solution is interpreted in the Skorohod sense, using Malliavin calculus. We consider two cases: (i) the regular noise, whose spatial covariance is given by the Riesz kernel of order $alpha in (0,d)$, in spatial dimension $dgeq 1$; (ii) the rough noise, which is fractional in space with Hurst index $H<1/2$, in spatial dimension $d=1$. We assume that the noise is colored in time. The similar problem for the white noise in time was considered in Bezdek (2016) and Giordano, Jolis and Quer-Sardanyons (2020).","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49662883","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 : 2023-05-04DOI: 10.1142/s0219493723500314
El Mountasar Billah Bouhadjar, M. Mnif
{"title":"Public Private Partnerships contract under moral hazard and ambiguous information","authors":"El Mountasar Billah Bouhadjar, M. Mnif","doi":"10.1142/s0219493723500314","DOIUrl":"https://doi.org/10.1142/s0219493723500314","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41467144","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 : 2023-04-28DOI: 10.1142/s0219493723500338
Ye-Jun Chen, H. Ding
{"title":"Remotely Almost Periodicity for SDEs under the Framework of Evolution System","authors":"Ye-Jun Chen, H. Ding","doi":"10.1142/s0219493723500338","DOIUrl":"https://doi.org/10.1142/s0219493723500338","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49561292","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 : 2023-04-28DOI: 10.1142/s0219493723500363
Yexing Chen, Yongluo Cao, Ruibiao Zou
{"title":"Uniformity of Singular Value Exponents for Typical Cocycles","authors":"Yexing Chen, Yongluo Cao, Ruibiao Zou","doi":"10.1142/s0219493723500363","DOIUrl":"https://doi.org/10.1142/s0219493723500363","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43631696","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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