Random Operators and Stochastic Equations最新文献

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}