In this paper we investigate the existence and uniqueness of solutions for a class of boundary value problem for fractional differential equations involving the Hadamard’s fractional derivative, by applying a nonlinear alternative of Leray–Schauder due to Frigon and Granas for contraction maps in Fréchet spaces.
{"title":"Existence results for boundary value problems of Hadamard fractional differential equations on unbounded domain","authors":"Mohamed Helal, Meriem Kerfouf, Fadila Semari","doi":"10.1515/rose-2024-2011","DOIUrl":"https://doi.org/10.1515/rose-2024-2011","url":null,"abstract":"\u0000 In this paper we investigate the existence and uniqueness of\u0000solutions for a class of boundary value problem for fractional differential equations\u0000involving the Hadamard’s fractional derivative, by applying a nonlinear alternative of\u0000Leray–Schauder due to Frigon and Granas for contraction maps in Fréchet spaces.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141013255","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}
In this paper, we have studied stochastic differential equations with unbounded delay in fractional power spaces perturbed by fractional Ornstein–Uhlenbeck process YH,ξ(t){{Y^{H,xi}}(t)} with H∈(12,1){Hin(frac{1}{2},1)}. Subsequently, the existence and uniqueness of mild solution of the considered equation have been proved with fixed-point theorem. Finally, we obtain the global attracting set of the considered equations by some stochastic analysis and inequality technique.
本文研究了分数幂空间中受分数 Ornstein-Uhlenbeck 过程 Y H , ξ ( t ) {{Y^{H,xi}}(t)} 扰动的具有无限制延迟的随机微分方程，H∈ ( 1 2 , 1 ) 。 {Hin(frac{1}{2},1)} 。随后，用定点定理证明了所考虑方程的温和解的存在性和唯一性。最后，我们通过一些随机分析和不等式技术得到了所考虑方程的全局吸引集。
{"title":"Global attracting set of stochastic differential equations with unbounded delay driven by fractional Ornstein–Uhlenbeck process","authors":"Yarong Peng, Liping Xu, Zhi Li","doi":"10.1515/rose-2024-2004","DOIUrl":"https://doi.org/10.1515/rose-2024-2004","url":null,"abstract":"\u0000 <jats:p>In this paper, we have studied stochastic differential equations with unbounded delay in fractional power spaces perturbed by fractional Ornstein–Uhlenbeck process <jats:inline-formula id=\"j_rose-2024-2004_ineq_9999\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:msup>\u0000 <m:mi>Y</m:mi>\u0000 <m:mrow>\u0000 <m:mi>H</m:mi>\u0000 <m:mo>,</m:mo>\u0000 <m:mi>ξ</m:mi>\u0000 </m:mrow>\u0000 </m:msup>\u0000 <m:mo></m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mi>t</m:mi>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_rose-2024-2004_eq_0271.png\" />\u0000 <jats:tex-math>{{Y^{H,xi}}(t)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula> with <jats:inline-formula id=\"j_rose-2024-2004_ineq_9998\">\u0000 <jats:alternatives>\u0000 <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\">\u0000 <m:mrow>\u0000 <m:mi>H</m:mi>\u0000 <m:mo>∈</m:mo>\u0000 <m:mrow>\u0000 <m:mo stretchy=\"false\">(</m:mo>\u0000 <m:mfrac>\u0000 <m:mn>1</m:mn>\u0000 <m:mn>2</m:mn>\u0000 </m:mfrac>\u0000 <m:mo>,</m:mo>\u0000 <m:mn>1</m:mn>\u0000 <m:mo stretchy=\"false\">)</m:mo>\u0000 </m:mrow>\u0000 </m:mrow>\u0000 </m:math>\u0000 <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_rose-2024-2004_eq_0135.png\" />\u0000 <jats:tex-math>{Hin(frac{1}{2},1)}</jats:tex-math>\u0000 </jats:alternatives>\u0000 </jats:inline-formula>. Subsequently, the existence and uniqueness of mild solution of the considered equation have been proved with fixed-point theorem. Finally, we obtain the global attracting set of the considered equations by some stochastic analysis and inequality technique.</jats:p>","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140664961","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}
A one-dimensional generalized backward stochastic differential equation with jumps and two barriers is the main objective of this paper. When the generators are monotone and the barriers are right continuous with left limits and completely separated, we prove the existence and uniqueness of a solution. As in application, we provide a probabilistic interpretation of a solution of a double obstacle problem of second-order parabolic integral-partial differential equations with nonlinear Neumann boundary conditions.
{"title":"Doubly reflected generalized BSDEs with jumps and an obstacle problem of parabolic IPDEs with nonlinear Neumann boundary conditions","authors":"Mohammed Elhachemy, M. El Otmani","doi":"10.1515/rose-2024-2002","DOIUrl":"https://doi.org/10.1515/rose-2024-2002","url":null,"abstract":"\u0000 A one-dimensional generalized backward stochastic differential equation with jumps and two barriers is the main objective of this paper.\u0000When the generators are monotone and the barriers are right continuous with left limits and completely separated, we prove the existence and uniqueness of a solution.\u0000As in application, we provide a probabilistic interpretation of a solution of a double obstacle problem of second-order parabolic integral-partial differential equations with nonlinear Neumann boundary conditions.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140420801","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}
Zakaria Boumezbeur, H. Boutabia, A. Redjil, O. Kebiri
In this paper, we study the differentiability of solutions of neutral stochastic differential equations driven by G-Brownian motion with respect to parameter. Under suitable assumptions, we show that solutions are differentiable with respect to the parameter which appears in the initial data. In addition, the stochastic differential equation of the derivative is given and the existence-uniqueness of solution is proved. Moreover, an example to illustrate the theoretically obtained results is presented.
本文研究了由 G 布朗运动驱动的中性随机微分方程解关于参数的可微性。在适当的假设条件下，我们证明了解是可微的，且与初始数据中出现的参数有关。此外，还给出了导数的随机微分方程，并证明了解的唯一性。此外，我们还给出了一个例子来说明理论上得到的结果。
{"title":"Differentiability of G-neutral stochastic differential equations with respect to parameter","authors":"Zakaria Boumezbeur, H. Boutabia, A. Redjil, O. Kebiri","doi":"10.1515/rose-2024-2005","DOIUrl":"https://doi.org/10.1515/rose-2024-2005","url":null,"abstract":"\u0000 In this paper, we study the\u0000differentiability of solutions of neutral stochastic differential equations\u0000driven by G-Brownian motion with respect to parameter. Under suitable\u0000assumptions, we show that solutions are differentiable with respect to the\u0000parameter which appears in the initial data. In addition, the stochastic\u0000differential equation of the derivative is given and the\u0000existence-uniqueness of solution is proved. Moreover, an example to\u0000illustrate the theoretically obtained results is presented.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140447001","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}
We study a family of representations of the canonical commutation relations (CCR)-algebra, which we refer to as “admissible,” with an infinite number of degrees of freedom. We establish a direct correlation between each admissible representation and a corresponding Gaussian stochastic calculus. Moreover, we derive the operators of Malliavin’s calculus of variation using an algebraic approach, which differs from the conventional methods. The Fock-vacuum representation leads to a maximal symmetric pair. This duality perspective offers the added advantage of resolving issues related to unbounded operators and dense domains much more easily than with alternative approaches.
{"title":"The operators of stochastic calculus","authors":"Palle Jorgensen, James Tian","doi":"10.1515/rose-2024-2007","DOIUrl":"https://doi.org/10.1515/rose-2024-2007","url":null,"abstract":"\u0000 We study a family of representations of the canonical commutation\u0000relations (CCR)-algebra, which we refer to as “admissible,”\u0000with an infinite number of degrees of freedom. We establish a direct\u0000correlation between each admissible representation and a corresponding\u0000Gaussian stochastic calculus. Moreover, we derive the operators of\u0000Malliavin’s calculus of variation using an algebraic approach, which\u0000differs from the conventional methods. The Fock-vacuum representation\u0000leads to a maximal symmetric pair. This duality perspective offers\u0000the added advantage of resolving issues related to unbounded operators\u0000and dense domains much more easily than with alternative approaches.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140445368","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}
In this paper, random optimization problems are investigated. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.
本文研究了随机优化问题。提出了一些确保随机优化问题存在随机解的充分条件。
{"title":"The existence of random solutions to random optimization problems","authors":"T. N. Anh, Dao Khac Huan","doi":"10.1515/rose-2024-2003","DOIUrl":"https://doi.org/10.1515/rose-2024-2003","url":null,"abstract":"\u0000 In this paper, random optimization problems are investigated. Some sufficient conditions ensuring the existence of random solutions to random optimization problems are proposed.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140449182","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}
Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Bus. Econom. Statist. 14 1996, 2, 139–151]; these models have gained considerable interest and continued to attract the attention of researchers. This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well.
Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) 模型是由 Bollerslev 和 Ghysels 提出的 [T. Bollerslev and E. Ghysels, Periodic autoregressive conditionally heteroscedasticity, J. PGARCH]。Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity,J. Bus.Bus.统计学家。统计学家。本文致力于将标准绝对值 GARCH（AVGARCH）模型扩展为周期性时变系数（PAVGARCH）模型。在这一类模型中，允许参数在不同制度之间切换。首先，我们给出了确保静态解（周期意义上的）存在的必要条件和充分条件。其次，我们开发了一种估计 PAVGARCH 模型的准极大似然（QML）估计方法。在温和的正则性条件下，研究了估计器的强一致性和渐近正则性，要求误差项具有严格的静态性和一定阶矩的有限性。接下来，我们介绍了一组数值实验，说明了我们理论结果的实际意义。最后，我们将模型应用于两种外汇汇率：阿尔及利亚第纳尔对欧洲货币欧元（欧元/第纳尔）和美国货币美元（美元/第纳尔）。这项实证工作表明，我们的方法也优于并很好地拟合了数据。
{"title":"QMLE for periodic absolute value GARCH models","authors":"Walid Slimani, Ines Lescheb, Mouloud Cherfaoui","doi":"10.1515/rose-2023-2027","DOIUrl":"https://doi.org/10.1515/rose-2023-2027","url":null,"abstract":"\u0000 Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels,\u0000Periodic autoregressive conditional heteroscedasticity,\u0000J. Bus. Econom. Statist. 14 1996, 2, 139–151];\u0000these models have gained considerable interest and continued to attract the attention of researchers.\u0000This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139876235","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}
Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Bus. Econom. Statist. 14 1996, 2, 139–151]; these models have gained considerable interest and continued to attract the attention of researchers. This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well.
Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) 模型是由 Bollerslev 和 Ghysels 提出的 [T. Bollerslev and E. Ghysels, Periodic autoregressive conditionally heteroscedasticity, J. PGARCH]。Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity,J. Bus.Bus.统计学家。统计学家。本文致力于将标准绝对值 GARCH（AVGARCH）模型扩展为周期性时变系数（PAVGARCH）模型。在这一类模型中，允许参数在不同制度之间切换。首先，我们给出了确保静态解（周期意义上的）存在的必要条件和充分条件。其次，我们开发了一种估计 PAVGARCH 模型的准极大似然（QML）估计方法。在温和的正则性条件下，研究了估计器的强一致性和渐近正则性，要求误差项具有严格的静态性和一定阶矩的有限性。接下来，我们介绍了一组数值实验，说明了我们理论结果的实际意义。最后，我们将模型应用于两种外汇汇率：阿尔及利亚第纳尔对欧洲货币欧元（欧元/第纳尔）和美国货币美元（美元/第纳尔）。这项实证工作表明，我们的方法也优于并很好地拟合了数据。
{"title":"QMLE for periodic absolute value GARCH models","authors":"Walid Slimani, Ines Lescheb, Mouloud Cherfaoui","doi":"10.1515/rose-2023-2027","DOIUrl":"https://doi.org/10.1515/rose-2023-2027","url":null,"abstract":"\u0000 Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels,\u0000Periodic autoregressive conditional heteroscedasticity,\u0000J. Bus. Econom. Statist. 14 1996, 2, 139–151];\u0000these models have gained considerable interest and continued to attract the attention of researchers.\u0000This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139816568","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}
We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter H ∈ ( 0 , 1 ) {Hin(0,1)} , in the case where the set of the control domain is convex. We provide an estimation of the solution and establish the necessary and sufficient optimality conditions in the form of the stochastic maximum principle. We apply the theory to solve a linear quadratic stochastic control problem.
{"title":"Stochastic controls of fractional Brownian motion","authors":"Ikram Hamed, A. Chala","doi":"10.1515/rose-2023-2025","DOIUrl":"https://doi.org/10.1515/rose-2023-2025","url":null,"abstract":"\u0000 We consider a stochastic control problem for a non-linear forward-backward stochastic differential equation driven by fractional Brownian motion, with Hurst parameter \u0000 \u0000 \u0000 \u0000 H\u0000 ∈\u0000 \u0000 (\u0000 0\u0000 ,\u0000 1\u0000 )\u0000 \u0000 \u0000 \u0000 \u0000 {Hin(0,1)}\u0000 \u0000 , in the case where the set of the control domain is convex. We provide an estimation of the solution and establish the necessary and sufficient optimality conditions in the form of the stochastic maximum principle.\u0000We apply the theory to solve a linear quadratic stochastic control problem.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139684323","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 study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.
{"title":"On a reaction diffusion problem with a moving impulse on boundary","authors":"Alioune Coulibaly","doi":"10.1515/rose-2023-2023","DOIUrl":"https://doi.org/10.1515/rose-2023-2023","url":null,"abstract":"Abstract We study an asymptotic problem of a semilinear partial differential equation (PDE) with Neumann boundary condition, periodic coefficients and highly oscillating drift and nonlinear terms. Our analysis focuses on the double limiting behavior of the PDE-solution perturbed by ε (viscosity parameter) and δ (scaling coefficient) both tending to zero. To do so, we state basic properties of the large deviations principle (LDP) and we express the logarithmic asymptotic of the PDE-solution. Particularly, we provide it for the case when ε converges more quickly than δ.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139438264","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}
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