Abstract One generalization of the G-density of the global law for random matrices whose entries are independent is founded.
摘要建立了项独立随机矩阵全局律g密度的一个推广。
{"title":"Sombrero law","authors":"Vyacheslav L. Girko","doi":"10.1515/rose-2022-2085","DOIUrl":"https://doi.org/10.1515/rose-2022-2085","url":null,"abstract":"Abstract One generalization of the G-density of the global law for random matrices whose entries are independent is founded.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"215 - 219"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44531997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This manuscript investigates the approximate controllability for a wide range of infinite-delayed semilinear stochastic differential inclusions. First, we construct the expression for a mild solution in terms of the fundamental solution. Then, employing the fixed point theorem for multivalued maps, we formulate a set of sufficient conditions to assure the existence of a solution for the aforementioned system. Further, the approximate controllability for the semilinear stochastic differential inclusion is investigated under the condition that the associated linear deterministic control system is approximately controllable. The discussed results are more general and a continuation of the ongoing research on this issue. Finally, an example is included to highlight the applicability of the considered results.
{"title":"Approximate controllability for a new class of stochastic functional differential inclusions with infinite delay","authors":"Surendra Kumar, S. Yadav","doi":"10.1515/rose-2022-2088","DOIUrl":"https://doi.org/10.1515/rose-2022-2088","url":null,"abstract":"Abstract This manuscript investigates the approximate controllability for a wide range of infinite-delayed semilinear stochastic differential inclusions. First, we construct the expression for a mild solution in terms of the fundamental solution. Then, employing the fixed point theorem for multivalued maps, we formulate a set of sufficient conditions to assure the existence of a solution for the aforementioned system. Further, the approximate controllability for the semilinear stochastic differential inclusion is investigated under the condition that the associated linear deterministic control system is approximately controllable. The discussed results are more general and a continuation of the ongoing research on this issue. Finally, an example is included to highlight the applicability of the considered results.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"221 - 239"},"PeriodicalIF":0.4,"publicationDate":"2022-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43227470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The generalized Brownian bridge X a , b , T {X^{a,b,T}} from a to b of length T was used in several fields such as in mathematical finance, biology and statistics. In this paper, we study the following stochastic properties and characteristics of this process: The Hölder continuity, the self-similarity, the quadratic variation, the Markov property, the stationarity of the increments, and the α-differentiability of the trajectories.
{"title":"Some results on the generalized Brownian bridge","authors":"S. Hadiri, A. Sghir","doi":"10.1515/rose-2022-2082","DOIUrl":"https://doi.org/10.1515/rose-2022-2082","url":null,"abstract":"Abstract The generalized Brownian bridge X a , b , T {X^{a,b,T}} from a to b of length T was used in several fields such as in mathematical finance, biology and statistics. In this paper, we study the following stochastic properties and characteristics of this process: The Hölder continuity, the self-similarity, the quadratic variation, the Markov property, the stationarity of the increments, and the α-differentiability of the trajectories.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"197 - 204"},"PeriodicalIF":0.4,"publicationDate":"2022-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43222711","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we prove the existence of a square-mean inertial manifold for a class of semilinear stochastic differential equations in a real separable Hilbert space. An example is given to illustrate our results.
{"title":"Square-mean inertial manifolds for stochastic differential equations","authors":"Thi Oanh Le","doi":"10.1515/rose-2022-2078","DOIUrl":"https://doi.org/10.1515/rose-2022-2078","url":null,"abstract":"Abstract In this paper, we prove the existence of a square-mean inertial manifold for a class of semilinear stochastic differential equations in a real separable Hilbert space. An example is given to illustrate our results.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"149 - 159"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43878900","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider a problem of parameter estimation for the fractional Ornstein–Uhlenbeck model given by the stochastic differential equation d X t = - θ X t d t + d B t H {dX_{t}=-theta X_{t}dt+dB_{t}^{H}} , t ≥ 0 {tgeq 0} , where θ > 0 {theta>0} is an unknown parameter to be estimated and B H {B^{H}} is a fractional Brownian motion with Hurst parameter H ∈ ( 0 , 1 ) {Hin(0,1)} . We provide an estimator for θ, and then we study its strong consistency and asymptotic normality. The main tool in our proofs is the paper [I. Nourdin, D. Nualart and G. Peccati, The Breuer–Major theorem in total variation: Improved rates under minimal regularity, Stochastic Process. Appl. 131 2021, 1–20].
考虑分数阶Ornstein-Uhlenbeck模型的参数估计问题，该模型由随机微分方程d ＿ X t=- θ ＿ X t ＿ d ＿t +d ＿ B＿t H {dX＿t{=-}theta X＿tdt{+}dB＿t{^}H{, t≥0 }}t{geq 0给出，}其中θ >0{theta >0}是一个待估计的未知参数，B H{ B^{H}}是一个带有Hurst参数H∈(0,1){Hin(0,1)的分数阶布朗运动}。给出了θ的一个估计量，并研究了它的强相合性和渐近正态性。我们证明的主要工具是论文[1]。努尔丁，D. Nualart和G. Peccati，总变分的布鲁尔-梅奇定理:最小规则下的改进率，随机过程。中国科学:地球科学[j]。
{"title":"On parameter estimation of fractional Ornstein–Uhlenbeck process","authors":"Fatima-Ezzahra Farah","doi":"10.1515/rose-2022-2079","DOIUrl":"https://doi.org/10.1515/rose-2022-2079","url":null,"abstract":"Abstract We consider a problem of parameter estimation for the fractional Ornstein–Uhlenbeck model given by the stochastic differential equation d X t = - θ X t d t + d B t H {dX_{t}=-theta X_{t}dt+dB_{t}^{H}} , t ≥ 0 {tgeq 0} , where θ > 0 {theta>0} is an unknown parameter to be estimated and B H {B^{H}} is a fractional Brownian motion with Hurst parameter H ∈ ( 0 , 1 ) {Hin(0,1)} . We provide an estimator for θ, and then we study its strong consistency and asymptotic normality. The main tool in our proofs is the paper [I. Nourdin, D. Nualart and G. Peccati, The Breuer–Major theorem in total variation: Improved rates under minimal regularity, Stochastic Process. Appl. 131 2021, 1–20].","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"161 - 170"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42743997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider an infinite horizon optimal control of a system where the dynamics evolve according to a mean-field stochastic differential equation and the cost functional is also of mean-field type. These are systems where the coefficients depend not only on the state variable, but also on its marginal distribution via some linear functional. Under some concavity assumptions on the coefficients as well as on the Hamiltonian, we are able to prove a verification theorem, which gives a sufficient condition for optimality for a given admissible control. In the absence of concavity, we prove a necessary condition for optimality in the form of a weak Pontryagin maximum principle, given in terms of stationarity of the Hamiltonian.
{"title":"Necessary and sufficient conditions in optimal control of mean-field stochastic differential equations with infinite horizon","authors":"Abdallah Roubi, Mohamed Amine Mezerdi","doi":"10.1515/rose-2022-2081","DOIUrl":"https://doi.org/10.1515/rose-2022-2081","url":null,"abstract":"Abstract We consider an infinite horizon optimal control of a system where the dynamics evolve according to a mean-field stochastic differential equation and the cost functional is also of mean-field type. These are systems where the coefficients depend not only on the state variable, but also on its marginal distribution via some linear functional. Under some concavity assumptions on the coefficients as well as on the Hamiltonian, we are able to prove a verification theorem, which gives a sufficient condition for optimality for a given admissible control. In the absence of concavity, we prove a necessary condition for optimality in the form of a weak Pontryagin maximum principle, given in terms of stationarity of the Hamiltonian.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"183 - 195"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42064275","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We consider the three-dimensional stochastic Leray-α model with homogeneous Dirichlet boundary conditions and infinite-dimensional Wiener process. We first study the mean square and pathwise exponential stability of a stationary solution to the model. Then we show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback control with support large enough.
{"title":"Asymptotic behavior of solutions to the three-dimensional stochastic Leray-α model","authors":"N. Thanh, T. Tuan","doi":"10.1515/rose-2022-2077","DOIUrl":"https://doi.org/10.1515/rose-2022-2077","url":null,"abstract":"Abstract We consider the three-dimensional stochastic Leray-α model with homogeneous Dirichlet boundary conditions and infinite-dimensional Wiener process. We first study the mean square and pathwise exponential stability of a stationary solution to the model. Then we show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback control with support large enough.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"137 - 148"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44545785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we consider a class of fractional impulsive neutral stochastic functional differential equations with infinite delay driven by a fractional Brownian motion in a real separable Hilbert space. We prove the existence of mild solutions by using stochastic analysis and a fixed-point strategy.
{"title":"Existence of solutions for fractional impulsive neutral functional differential equations driven by fractional Brownian motion","authors":"A. Lahmoudi, E. Lakhel","doi":"10.1515/rose-2022-2080","DOIUrl":"https://doi.org/10.1515/rose-2022-2080","url":null,"abstract":"Abstract In this paper, we consider a class of fractional impulsive neutral stochastic functional differential equations with infinite delay driven by a fractional Brownian motion in a real separable Hilbert space. We prove the existence of mild solutions by using stochastic analysis and a fixed-point strategy.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"171 - 182"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42621094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we are concerned with an optimal control problem where the system is driven by a G-stochastic differential equation, where an admissible set of controls is convex. We establish necessary as well as sufficient optimality conditions for this model. At the end of this work, we illustrate our main result by giving an example that deals with the linear-quadratic problem.
{"title":"Stochastic maximum principle for optimal control problem under G-expectation utility","authors":"Meriyam Dassa, A. Chala","doi":"10.1515/rose-2022-2076","DOIUrl":"https://doi.org/10.1515/rose-2022-2076","url":null,"abstract":"Abstract In this paper, we are concerned with an optimal control problem where the system is driven by a G-stochastic differential equation, where an admissible set of controls is convex. We establish necessary as well as sufficient optimality conditions for this model. At the end of this work, we illustrate our main result by giving an example that deals with the linear-quadratic problem.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"30 1","pages":"121 - 135"},"PeriodicalIF":0.4,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42764913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：