Pub Date : 2022-05-13DOI: 10.1080/07362994.2022.2071739
Mengyuan Kong, Yinghui Shi, Xiaobin Sun
Abstract In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical α-stable process, where Then by the method of the Khasminskii’s time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical α-stable processes. Meanwhile, we obtain a specific strong convergence rate.
{"title":"Well-posedness and averaging principle of McKean-Vlasov SPDEs driven by cylindrical α-stable process","authors":"Mengyuan Kong, Yinghui Shi, Xiaobin Sun","doi":"10.1080/07362994.2022.2071739","DOIUrl":"https://doi.org/10.1080/07362994.2022.2071739","url":null,"abstract":"Abstract In this paper, we first study the well-posedness of a class of McKean-Vlasov stochastic partial differential equations driven by cylindrical α-stable process, where Then by the method of the Khasminskii’s time discretization, we prove the averaging principle of a class of multiscale McKean-Vlasov stochastic partial differential equations driven by cylindrical α-stable processes. Meanwhile, we obtain a specific strong convergence rate.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"672 - 692"},"PeriodicalIF":1.3,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46137303","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 : 2022-05-12DOI: 10.1080/07362994.2022.2071738
Xuemei Li, Xinge Liu
Abstract In this paper, the approximate controllability of Hilfer fractional stochastic evolution inclusion with nonlocal conditions is investigated. By using fractional calculus, semigroups theory, stochastic analysis and the fixed point theorem for multi-valued maps, a new sufficient condition for the existence of mild solution of the Hilfer fractional stochastic system in the space of weighted continuous functions is derived. Furthermore, a novel sufficient condition for the approximate controllability of the Hilfer fractional stochastic evolution inclusion with nonlocal conditions is established. Finally, an example is presented to illustrate the main results.
{"title":"Approximate controllability for Hilfer fractional stochastic evolution inclusion with nonlocal conditions","authors":"Xuemei Li, Xinge Liu","doi":"10.1080/07362994.2022.2071738","DOIUrl":"https://doi.org/10.1080/07362994.2022.2071738","url":null,"abstract":"Abstract In this paper, the approximate controllability of Hilfer fractional stochastic evolution inclusion with nonlocal conditions is investigated. By using fractional calculus, semigroups theory, stochastic analysis and the fixed point theorem for multi-valued maps, a new sufficient condition for the existence of mild solution of the Hilfer fractional stochastic system in the space of weighted continuous functions is derived. Furthermore, a novel sufficient condition for the approximate controllability of the Hilfer fractional stochastic evolution inclusion with nonlocal conditions is established. Finally, an example is presented to illustrate the main results.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"647 - 671"},"PeriodicalIF":1.3,"publicationDate":"2022-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59595869","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 : 2022-05-01DOI: 10.1080/07362994.2022.2068580
Kai Liu
Abstract This is a continuation of [5] which is concerned about the regularity property of stochastic convolutions for abstract linear stochastic retarded differential equations with unbounded operators on delay terms. In this work, we improve and generalize the main results in [5] by considering those delay operators which may have the same order as the infinitesimal generator of the system under consideration. To this end, we need restrict the weight function of distributed delay term to be Hölder continuous type in this system.
{"title":"A note on regularity property of stochastic convolutions for a class of functional differential equations","authors":"Kai Liu","doi":"10.1080/07362994.2022.2068580","DOIUrl":"https://doi.org/10.1080/07362994.2022.2068580","url":null,"abstract":"Abstract This is a continuation of [5] which is concerned about the regularity property of stochastic convolutions for abstract linear stochastic retarded differential equations with unbounded operators on delay terms. In this work, we improve and generalize the main results in [5] by considering those delay operators which may have the same order as the infinitesimal generator of the system under consideration. To this end, we need restrict the weight function of distributed delay term to be Hölder continuous type in this system.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"631 - 646"},"PeriodicalIF":1.3,"publicationDate":"2022-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43341972","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 : 2022-04-28DOI: 10.1080/07362994.2022.2068579
C. Makasu
Abstract We prove a stochastic version of the Gronwall lemma assuming that the underlying martingale has a terminal random value in Lp , where The proof of the present result is mainly based on a sharp martingale inequality of the Doob-type.
{"title":"A note on the stochastic version of the Gronwall lemma","authors":"C. Makasu","doi":"10.1080/07362994.2022.2068579","DOIUrl":"https://doi.org/10.1080/07362994.2022.2068579","url":null,"abstract":"Abstract We prove a stochastic version of the Gronwall lemma assuming that the underlying martingale has a terminal random value in Lp , where The proof of the present result is mainly based on a sharp martingale inequality of the Doob-type.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"626 - 629"},"PeriodicalIF":1.3,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48184498","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 : 2022-04-24DOI: 10.1080/07362994.2022.2064306
Kamal Hiderah, Mohamed Bourza
Abstract In this article, we aim to present the Carathéodory scheme for a class of perturbed stochastic differential equations with reflecting boundary (PSDERB). It is shown that the Carathéodory approximate solutions converge to the unique solution of this class of PSDERB. The existence and pathwise uniqueness theorem for this class of PSDERB are established under irregular coefficients.
{"title":"Carathéodory approximate solutions for a class of perturbed reflected stochastic differential equations with irregular coefficients","authors":"Kamal Hiderah, Mohamed Bourza","doi":"10.1080/07362994.2022.2064306","DOIUrl":"https://doi.org/10.1080/07362994.2022.2064306","url":null,"abstract":"Abstract In this article, we aim to present the Carathéodory scheme for a class of perturbed stochastic differential equations with reflecting boundary (PSDERB). It is shown that the Carathéodory approximate solutions converge to the unique solution of this class of PSDERB. The existence and pathwise uniqueness theorem for this class of PSDERB are established under irregular coefficients.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"604 - 625"},"PeriodicalIF":1.3,"publicationDate":"2022-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44289203","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 : 2022-03-28DOI: 10.1080/07362994.2023.2213755
Po-Han Hsu, P. Sundar
Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we introduce a family of regularized equations and investigate the asymptotic behavior of the regularized equations first. The existence an ergodic measure for the regularized system is established via the Krylov-Bogolyubov method. Then the existence of an stationary measure to the original system is obtained by extracting a limit from the ergodic measures of the family of the regularized system.
{"title":"Ergodicity for three-dimensional stochastic Navier–Stokes equations with Markovian switching","authors":"Po-Han Hsu, P. Sundar","doi":"10.1080/07362994.2023.2213755","DOIUrl":"https://doi.org/10.1080/07362994.2023.2213755","url":null,"abstract":"Asymptotic behavior of the three-dimensional stochastic Navier-Stokes equations with Markov switching in additive noises is studied for incompressible fluid flow in a bounded domain in the three-dimensional space. To study such a system, we introduce a family of regularized equations and investigate the asymptotic behavior of the regularized equations first. The existence an ergodic measure for the regularized system is established via the Krylov-Bogolyubov method. Then the existence of an stationary measure to the original system is obtained by extracting a limit from the ergodic measures of the family of the regularized system.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47907129","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 : 2022-03-23DOI: 10.1080/07362994.2022.2047726
Akli O. L. Babi, M. Dieye, O. M. Pamen
Abstract In this work, we prove strong convergence on small time interval of order for arbitrarily small of the Euler-Maruyama approximation for additive Brownian motion with Hölder continuous drift satisfying a linear growth condition. The proof is based on direct estimations of functional of the Euler-Maruyama approximation. The order of convergence does not depend on the Hölder index of the drift, thus generalizing the results obtained in [10] to both Linear growth and to an optimal convergence order.
{"title":"Strong convergence of the Euler-Maruyama approximation for SDEs with unbounded drift","authors":"Akli O. L. Babi, M. Dieye, O. M. Pamen","doi":"10.1080/07362994.2022.2047726","DOIUrl":"https://doi.org/10.1080/07362994.2022.2047726","url":null,"abstract":"Abstract In this work, we prove strong convergence on small time interval of order for arbitrarily small of the Euler-Maruyama approximation for additive Brownian motion with Hölder continuous drift satisfying a linear growth condition. The proof is based on direct estimations of functional of the Euler-Maruyama approximation. The order of convergence does not depend on the Hölder index of the drift, thus generalizing the results obtained in [10] to both Linear growth and to an optimal convergence order.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"545 - 563"},"PeriodicalIF":1.3,"publicationDate":"2022-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41911815","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 : 2022-03-09DOI: 10.1080/07362994.2022.2038624
Zhang Chen, Dandan Yang, Shitao Zhong
Abstract This work is devoted to stochastic reaction-diffusion lattice system driven by Lévy noises when the drift and diffusion terms are locally Lipschitz continuous. First, we investigate the existence and uniqueness of solutions of such system as well as weak pullback mean random attractors. Then the existence of periodic measures is obtained by the idea of uniform tail-estimates and Krylov-Bogolyubov’s method. Under further conditions, we establish the uniqueness and the exponentially mixing property of periodic measure. Finally, the limit behavior of periodic measures is investigated for stochastic lattice system driven by Lévy noises with respect to noise intensities.
{"title":"Weak mean attractor and periodic measure for stochastic lattice systems driven by Lévy noises","authors":"Zhang Chen, Dandan Yang, Shitao Zhong","doi":"10.1080/07362994.2022.2038624","DOIUrl":"https://doi.org/10.1080/07362994.2022.2038624","url":null,"abstract":"Abstract This work is devoted to stochastic reaction-diffusion lattice system driven by Lévy noises when the drift and diffusion terms are locally Lipschitz continuous. First, we investigate the existence and uniqueness of solutions of such system as well as weak pullback mean random attractors. Then the existence of periodic measures is obtained by the idea of uniform tail-estimates and Krylov-Bogolyubov’s method. Under further conditions, we establish the uniqueness and the exponentially mixing property of periodic measure. Finally, the limit behavior of periodic measures is investigated for stochastic lattice system driven by Lévy noises with respect to noise intensities.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"509 - 544"},"PeriodicalIF":1.3,"publicationDate":"2022-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42524403","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 : 2022-03-08DOI: 10.1080/07362994.2022.2144374
C. Fonseca-Mora
Let Φ a locally convex space and Ψ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces Φ ′ and Ψ ′ . In this work we introduce sufficient conditions for time regularity properties of the Ψ ′ -valued stochastic convolution R t 0 R U S ( t − r ) ′ R ( r, u ) M ( dr, du ), t ∈ [0 , T ], where ( S ( t ) : t ≥ 0) is a C 0 -semigroup on Ψ, R ( r, ω, u ) is a suitable operator form Φ ′ into Ψ ′ and M is a cylindrical-martingale valued measure on Φ ′ . Our result is latter applied to study time regularity of solutions to Ψ ′ -valued stochastic evolutions equations. 2020 Mathematics Subject Classification: 60G17, 60H05, 60H15, 60G20.
设Φ是局部凸空间，Ψ是具有对偶空间Φ′和Ψ′的拟完全、出生论核空间（光滑函数和分布的相似空间）。在这项工作中，我们引入了Ψ′值随机卷积R t0 R U S（t−R）′R（R，U）M（dr，du），t∈[0，t]的时间正则性性质的充分条件，其中（S（t）：t≥0）是Ψ上的C0-半群，R（R，ω，U）是Φ′到Ψ′的合适算子，M是Φ′上的圆柱鞅值测度。我们的结果应用于研究Ψ′值随机演化方程解的时间正则性。2020数学学科分类：60G17、60H05、60H15、60G20。
{"title":"Time regularity of stochastic convolutions and stochastic evolution equations in duals of nuclear spaces","authors":"C. Fonseca-Mora","doi":"10.1080/07362994.2022.2144374","DOIUrl":"https://doi.org/10.1080/07362994.2022.2144374","url":null,"abstract":"Let Φ a locally convex space and Ψ be a quasi-complete, bornological, nuclear space (like spaces of smooth functions and distributions) with dual spaces Φ ′ and Ψ ′ . In this work we introduce sufficient conditions for time regularity properties of the Ψ ′ -valued stochastic convolution R t 0 R U S ( t − r ) ′ R ( r, u ) M ( dr, du ), t ∈ [0 , T ], where ( S ( t ) : t ≥ 0) is a C 0 -semigroup on Ψ, R ( r, ω, u ) is a suitable operator form Φ ′ into Ψ ′ and M is a cylindrical-martingale valued measure on Φ ′ . Our result is latter applied to study time regularity of solutions to Ψ ′ -valued stochastic evolutions equations. 2020 Mathematics Subject Classification: 60G17, 60H05, 60H15, 60G20.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49203139","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 : 2022-02-02DOI: 10.1080/07362994.2022.2029712
F. Delgado-Vences, J. J. Pavon-Español
Abstract In this paper, we study asymptotic properties of the maximum likelihood estimator (MLE) for the speed of a stochastic wave equation. We follow a well-known spectral approach to write the solution as a Fourier series, then we project the solution to a N-finite dimensional space and find the estimator as a function of the time and N. We then show consistency of the MLE using classical stochastic analysis. Afterward, we prove the asymptotic normality using the Malliavin–Stein method. We also study asymptotic properties of a discretized version of the MLE for the parameter. We provide this asymptotic analysis of the proposed estimator as the number of Fourier modes, N, used in the estimation and the observation time go to infinity. Finally, we illustrate the theoretical results with some numerical experiments.
{"title":"Statistical inference for a stochastic wave equation with Malliavin–Stein method","authors":"F. Delgado-Vences, J. J. Pavon-Español","doi":"10.1080/07362994.2022.2029712","DOIUrl":"https://doi.org/10.1080/07362994.2022.2029712","url":null,"abstract":"Abstract In this paper, we study asymptotic properties of the maximum likelihood estimator (MLE) for the speed of a stochastic wave equation. We follow a well-known spectral approach to write the solution as a Fourier series, then we project the solution to a N-finite dimensional space and find the estimator as a function of the time and N. We then show consistency of the MLE using classical stochastic analysis. Afterward, we prove the asymptotic normality using the Malliavin–Stein method. We also study asymptotic properties of a discretized version of the MLE for the parameter. We provide this asymptotic analysis of the proposed estimator as the number of Fourier modes, N, used in the estimation and the observation time go to infinity. Finally, we illustrate the theoretical results with some numerical experiments.","PeriodicalId":49474,"journal":{"name":"Stochastic Analysis and Applications","volume":"41 1","pages":"447 - 473"},"PeriodicalIF":1.3,"publicationDate":"2022-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42216719","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}
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：