Pub Date : 2022-04-18DOI: 10.1142/s021949372250023x
Gregory Amali Paul Rose, M. Suvinthra, K. Balachandran
{"title":"Moderate deviations for stochastic Kuramoto-Sivashinsky equation","authors":"Gregory Amali Paul Rose, M. Suvinthra, K. Balachandran","doi":"10.1142/s021949372250023x","DOIUrl":"https://doi.org/10.1142/s021949372250023x","url":null,"abstract":"","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46272408","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 : 2022-04-18DOI: 10.1142/s0219493722400172
T. Caraballo, F. Morillas, J. Valero
In this paper, we study a stochastic system of differential equations with nonlocal discrete diffusion. For two types of noises, we study the existence of either positive or probability solutions. Also, we analyze the asymptotic behavior of solutions in the long term, showing that under suitable assumptions they tend to a neighborhood of the unique deterministic fixed point. Finally, we perform numerical simulations and discuss the application of the results to life tables for mortality in Spain.
{"title":"On a stochastic nonlocal system with discrete diffusion modeling life tables","authors":"T. Caraballo, F. Morillas, J. Valero","doi":"10.1142/s0219493722400172","DOIUrl":"https://doi.org/10.1142/s0219493722400172","url":null,"abstract":"In this paper, we study a stochastic system of differential equations with nonlocal discrete diffusion. For two types of noises, we study the existence of either positive or probability solutions. Also, we analyze the asymptotic behavior of solutions in the long term, showing that under suitable assumptions they tend to a neighborhood of the unique deterministic fixed point. Finally, we perform numerical simulations and discuss the application of the results to life tables for mortality in Spain.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46664635","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 : 2022-03-21DOI: 10.1142/s0219493722500198
Tuan A. Phan, Shuxun Wang, J. Tian
In this paper, we analyze a new Ito stochastic differential equation model for untreated human glioblastomas. The model was the best fit of the average growth and variance of 94 pairs of a data set. We show the existence and uniqueness of solutions in the positive spatial domain. When the model is restricted in the finite domain [Formula: see text], we show that the boundary point 0 is unattainable while the point [Formula: see text] is reflecting attainable. We prove there is a unique ergodic stationary distribution for any non-zero noise intensity, and obtain the explicit probability density function for the stationary distribution. By using Brownian bridge, we give a representation of the probability density function of the first passage time when the diffusion process defined by a solution passes the point [Formula: see text] firstly. We carry out numerical studies to illustrate our analysis. Our mathematical and numerical analysis confirms the soundness of our randomization of the deterministic model in that the stochastic model will set down to the deterministic model when the noise intensity approaches zero. We also give physical interpretation of our stochastic model and analysis.
{"title":"Analysis of a new stochastic Gompertz diffusion model for untreated human glioblastomas","authors":"Tuan A. Phan, Shuxun Wang, J. Tian","doi":"10.1142/s0219493722500198","DOIUrl":"https://doi.org/10.1142/s0219493722500198","url":null,"abstract":"In this paper, we analyze a new Ito stochastic differential equation model for untreated human glioblastomas. The model was the best fit of the average growth and variance of 94 pairs of a data set. We show the existence and uniqueness of solutions in the positive spatial domain. When the model is restricted in the finite domain [Formula: see text], we show that the boundary point 0 is unattainable while the point [Formula: see text] is reflecting attainable. We prove there is a unique ergodic stationary distribution for any non-zero noise intensity, and obtain the explicit probability density function for the stationary distribution. By using Brownian bridge, we give a representation of the probability density function of the first passage time when the diffusion process defined by a solution passes the point [Formula: see text] firstly. We carry out numerical studies to illustrate our analysis. Our mathematical and numerical analysis confirms the soundness of our randomization of the deterministic model in that the stochastic model will set down to the deterministic model when the noise intensity approaches zero. We also give physical interpretation of our stochastic model and analysis.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42349027","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 : 2022-03-15DOI: 10.1142/s0219493722500204
Oussama Elbarrimi
In this paper, we consider multidimensional mean-field stochastic differential equations where the coefficients depend on the law in the form of a Lebesgue integral with respect to the measure of the solution. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application for optimal control of diffusions. Namely, we propose a result on the approximation of the solution associated to a relaxed control.
{"title":"On the stability of mean-field stochastic differential equations with irregular expectation functional","authors":"Oussama Elbarrimi","doi":"10.1142/s0219493722500204","DOIUrl":"https://doi.org/10.1142/s0219493722500204","url":null,"abstract":"In this paper, we consider multidimensional mean-field stochastic differential equations where the coefficients depend on the law in the form of a Lebesgue integral with respect to the measure of the solution. Under the pathwise uniqueness property, we establish various strong stability results. As a consequence, we give an application for optimal control of diffusions. Namely, we propose a result on the approximation of the solution associated to a relaxed control.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44272461","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 : 2022-03-12DOI: 10.1142/s0219493722400093
Lin Shi, K. Lu, Xiaohu Wang
We investigate the limiting behavior of dynamics of non-autonomous stochastic FitzHugh–Nagumo equations driven by a nonlinear multiplicative colored noise on unbounded thin domains. We first establish the existence and uniqueness of random attractors for the equations on the thin domains and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.
{"title":"Limiting behavior of FitzHugh–Nagumo equations driven by colored noise on unbounded thin domains","authors":"Lin Shi, K. Lu, Xiaohu Wang","doi":"10.1142/s0219493722400093","DOIUrl":"https://doi.org/10.1142/s0219493722400093","url":null,"abstract":"We investigate the limiting behavior of dynamics of non-autonomous stochastic FitzHugh–Nagumo equations driven by a nonlinear multiplicative colored noise on unbounded thin domains. We first establish the existence and uniqueness of random attractors for the equations on the thin domains and their limit equations. Then, we establish the upper semicontinuity of these attractors when the thin domains collapse into a lower-dimensional unbounded domain.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49551845","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 : 2022-03-12DOI: 10.1142/s0219493722400081
Hongjun Gao, Shuaipeng Liu, Yeyu Xiao
In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.
{"title":"The limit behavior of SEIRS model in spatial grid","authors":"Hongjun Gao, Shuaipeng Liu, Yeyu Xiao","doi":"10.1142/s0219493722400081","DOIUrl":"https://doi.org/10.1142/s0219493722400081","url":null,"abstract":"In this paper, we study a SEIRS model with Neumann boundary condition for a population distributed in a spatial grid. We first discuss the existence and uniqueness of global positive solution with any given positive initial value. Next, we introduce the basic reproduction number of this model. Then we consider the relation between the system of PDE and the discrete ODE model. Finally, we consider the stochastic model and give two laws of large numbers.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48727975","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 : 2022-03-06DOI: 10.1142/s0219493722400408
Yi Wang, Jinxiang Yao
For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent λ max > 0 holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the C 1 -perturbation of the systems.
对于Banach空间上的强单调动力系统，我们证明了在测度论意义上，最大Lyapunov指数λ max >在一个shy集合上成立。这表明强单调动力系统不承认可观察到的混沌，混沌的概念是由L.S. Young提出的。进一步证明了系统在c1 -扰动下无可见混沌现象的鲁棒性。
{"title":"Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems","authors":"Yi Wang, Jinxiang Yao","doi":"10.1142/s0219493722400408","DOIUrl":"https://doi.org/10.1142/s0219493722400408","url":null,"abstract":"For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent λ max > 0 holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the C 1 -perturbation of the systems.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43171298","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 : 2022-02-25DOI: 10.1142/s0219493722500186
Wenya Wang, Zhongkai Guo
In this paper, a class of Itô–Doob stochastic fractional differential equations (Itô–Doob SFDEs) models are discussed. Using the time scale transformation method, we consider the averaging principle of the transformed equations and establish the relevant results. At the same time, we find that the optimal index for the original Itô–Doob SFDEs can be determined, the selection of such index is similar to the classical stochastic differential equations model.
{"title":"Optimal index and averaging principle for Itô–Doob stochastic fractional differential equations","authors":"Wenya Wang, Zhongkai Guo","doi":"10.1142/s0219493722500186","DOIUrl":"https://doi.org/10.1142/s0219493722500186","url":null,"abstract":"In this paper, a class of Itô–Doob stochastic fractional differential equations (Itô–Doob SFDEs) models are discussed. Using the time scale transformation method, we consider the averaging principle of the transformed equations and establish the relevant results. At the same time, we find that the optimal index for the original Itô–Doob SFDEs can be determined, the selection of such index is similar to the classical stochastic differential equations model.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43631343","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 : 2022-02-15DOI: 10.1142/s0219493723500132
Zachary Bezemek, K. Spiliopoulos
. We consider a fully-coupled slow-fast system of McKean-Vlasov SDEs with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy-Problem on the Wasserstein space that are of independent interest.
{"title":"Rate of homogenization for fully-coupled McKean-Vlasov SDEs","authors":"Zachary Bezemek, K. Spiliopoulos","doi":"10.1142/s0219493723500132","DOIUrl":"https://doi.org/10.1142/s0219493723500132","url":null,"abstract":". We consider a fully-coupled slow-fast system of McKean-Vlasov SDEs with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain related ergodic theorems and we gain results on the regularity of Poisson type of equations and of the associated Cauchy-Problem on the Wasserstein space that are of independent interest.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41559762","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 : 2022-01-26DOI: 10.1142/s0219493722500174
M. Dieye, Amadou Diop, M. McKibben
In this paper, we study the existence and continuous dependence on coefficients of mild solutions for first-order McKean–Vlasov integrodifferential equations with delay driven by a cylindrical Wiener process using resolvent operator theory and Wasserstein distance. Under the situation that the nonlinear term depends on the probability distribution of the state, the existence and uniqueness of solutions are established. An example illustrating the general results is included.
{"title":"Existence of solutions for mean-field integrodifferential equations with delay","authors":"M. Dieye, Amadou Diop, M. McKibben","doi":"10.1142/s0219493722500174","DOIUrl":"https://doi.org/10.1142/s0219493722500174","url":null,"abstract":"In this paper, we study the existence and continuous dependence on coefficients of mild solutions for first-order McKean–Vlasov integrodifferential equations with delay driven by a cylindrical Wiener process using resolvent operator theory and Wasserstein distance. Under the situation that the nonlinear term depends on the probability distribution of the state, the existence and uniqueness of solutions are established. An example illustrating the general results is included.","PeriodicalId":51170,"journal":{"name":"Stochastics and Dynamics","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63840385","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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