Abstract We discuss nonparametric estimation of a trend coefficient in models governed by a stochastic differential equation driven by a sub-fractional Brownian motion with small noise.
讨论了小噪声次分数布朗运动驱动的随机微分方程模型中趋势系数的非参数估计。
{"title":"Nonparametric estimation of trend for stochastic differential equations driven by sub-fractional Brownian motion","authors":"B. P. Rao","doi":"10.1515/rose-2020-2032","DOIUrl":"https://doi.org/10.1515/rose-2020-2032","url":null,"abstract":"Abstract We discuss nonparametric estimation of a trend coefficient in models governed by a stochastic differential equation driven by a sub-fractional Brownian motion with small noise.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"113 - 122"},"PeriodicalIF":0.4,"publicationDate":"2020-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46606731","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 paper contains the proof of the positivity of the top Lyapunov exponent for the multiplicative stochastic integrals related to the diffusion processes on the Lee algebra of the matrices with zero trace.
摘要本文证明了零迹矩阵Lee代数上与扩散过程有关的乘性随机积分的上李雅普诺夫指数的正性。
{"title":"Theorem of Furstenberg type for multiplicative stochastic integrals","authors":"N. Akanbay, S. Molchanov, Z. I. Suleimenova","doi":"10.1515/rose-2020-2035","DOIUrl":"https://doi.org/10.1515/rose-2020-2035","url":null,"abstract":"Abstract This paper contains the proof of the positivity of the top Lyapunov exponent for the multiplicative stochastic integrals related to the diffusion processes on the Lee algebra of the matrices with zero trace.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"163 - 175"},"PeriodicalIF":0.4,"publicationDate":"2020-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44087748","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 G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.
摘要在G-Lindeberg条件下，证明了随机矩阵中独立元素对的g -椭圆律。
{"title":"VICTORIA transform, RESPECT and REFORM methods for the proof of the G-Elliptic Law under G-Lindeberg condition and twice stochastic condition for the variances and covariances of the entries of some random matrices","authors":"V. Girko","doi":"10.1515/rose-2020-2034","DOIUrl":"https://doi.org/10.1515/rose-2020-2034","url":null,"abstract":"Abstract The G-Elliptic law under the G-Lindeberg condition for the independent pairs of the entries of a random matrix is proven.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"131 - 162"},"PeriodicalIF":0.4,"publicationDate":"2020-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43123408","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 wish to study a class of optimal controls for problems governed by forward-backward doubly stochastic differential equations (FBDSDEs). Firstly, we prove existence of optimal relaxed controls, which are measure-valued processes for nonlinear FBDSDEs, by using some tightness properties and weak convergence techniques on the space of Skorokhod 𝔻 {mathbb{D}} equipped with the S-topology of Jakubowski. Moreover, when the Roxin-type convexity condition is fulfilled, we prove that the optimal relaxed control is in fact strict. Secondly, we prove the existence of a strong optimal controls for a linear forward-backward doubly SDEs. Furthermore, we establish necessary as well as sufficient optimality conditions for a control problem of this kind of systems. This is the first theorem of existence of optimal controls that covers the forward-backward doubly systems.
{"title":"Existence of optimal controls for systems of controlled forward-backward doubly SDEs","authors":"Abdelhakim Ninouh, Boulakhras Gherbal, Nassima Berrouis","doi":"10.1515/rose-2020-2031","DOIUrl":"https://doi.org/10.1515/rose-2020-2031","url":null,"abstract":"Abstract We wish to study a class of optimal controls for problems governed by forward-backward doubly stochastic differential equations (FBDSDEs). Firstly, we prove existence of optimal relaxed controls, which are measure-valued processes for nonlinear FBDSDEs, by using some tightness properties and weak convergence techniques on the space of Skorokhod 𝔻 {mathbb{D}} equipped with the S-topology of Jakubowski. Moreover, when the Roxin-type convexity condition is fulfilled, we prove that the optimal relaxed control is in fact strict. Secondly, we prove the existence of a strong optimal controls for a linear forward-backward doubly SDEs. Furthermore, we establish necessary as well as sufficient optimality conditions for a control problem of this kind of systems. This is the first theorem of existence of optimal controls that covers the forward-backward doubly systems.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"112 - 93"},"PeriodicalIF":0.4,"publicationDate":"2020-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45679510","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 propose a new numerical method for 1-D backward stochastic differential equations (BSDEs for short) without using conditional expectations. The approximations of the solutions are obtained as solutions of a backward linear system generated by the terminal conditions. Our idea is inspired from the extended Kalman filter to non-linear system models by using a linear approximation around deterministic nominal reference trajectories.
{"title":"A new numerical method for 1-D backward stochastic differential equations without using conditional expectations","authors":"A. Sghir, Sokaina Hadiri","doi":"10.1515/rose-2020-2030","DOIUrl":"https://doi.org/10.1515/rose-2020-2030","url":null,"abstract":"Abstract In this paper, we propose a new numerical method for 1-D backward stochastic differential equations (BSDEs for short) without using conditional expectations. The approximations of the solutions are obtained as solutions of a backward linear system generated by the terminal conditions. Our idea is inspired from the extended Kalman filter to non-linear system models by using a linear approximation around deterministic nominal reference trajectories.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"79 - 91"},"PeriodicalIF":0.4,"publicationDate":"2020-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2030","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46248978","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 work, we prove some comparison theorems of anticipated backward doubly stochastic differential equations with non-Lipschitz coefficients.
摘要在这项工作中，我们证明了具有非Lipschitz系数的预期反向双随机微分方程的一些比较定理。
{"title":"Comparison theorems for anticipated backward doubly stochastic differential equations with non-Lipschitz coefficients","authors":"Sadibou Aidara","doi":"10.1515/rose-2020-2026","DOIUrl":"https://doi.org/10.1515/rose-2020-2026","url":null,"abstract":"Abstract In this work, we prove some comparison theorems of anticipated backward doubly stochastic differential equations with non-Lipschitz coefficients.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"19 - 26"},"PeriodicalIF":0.4,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47297858","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 problem of dynamic system control in the form of the liability fund with the functions of the insurance company working in the financial market and developing the advertising strategy is considered. The generalized Clark model describes the price of risk asset. The optimal controls of the financial market asset portfolio and the part of capital the insurance company spends on the carrying out of the advertising companies were found under which the merit functional takes the largest value. The price of such control also was found.
{"title":"The optimal control of the consumer fund with the functions of the insurance company under assumption of the work on the financial market with the advertising strategy","authors":"Valeriia Boldyrieva, Tetiana Zhmykhova","doi":"10.1515/rose-2020-2027","DOIUrl":"https://doi.org/10.1515/rose-2020-2027","url":null,"abstract":"Abstract The problem of dynamic system control in the form of the liability fund with the functions of the insurance company working in the financial market and developing the advertising strategy is considered. The generalized Clark model describes the price of risk asset. The optimal controls of the financial market asset portfolio and the part of capital the insurance company spends on the carrying out of the advertising companies were found under which the merit functional takes the largest value. The price of such control also was found.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"27 - 34"},"PeriodicalIF":0.4,"publicationDate":"2020-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2027","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48568436","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 backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.
{"title":"An optimal control of a risk-sensitive problem for backward doubly stochastic differential equations with applications","authors":"Dahbia Hafayed, A. Chala","doi":"10.1515/rose-2020-2024","DOIUrl":"https://doi.org/10.1515/rose-2020-2024","url":null,"abstract":"Abstract In this paper, we are concerned with an optimal control problem where the system is driven by a backward doubly stochastic differential equation with risk-sensitive performance functional. We generalized the result of Chala [A. Chala, Pontryagin’s risk-sensitive stochastic maximum principle for backward stochastic differential equations with application, Bull. Braz. Math. Soc. (N. S.) 48 2017, 3, 399–411] to a backward doubly stochastic differential equation by using the same contribution of Djehiche, Tembine and Tempone in [B. Djehiche, H. Tembine and R. Tempone, A stochastic maximum principle for risk-sensitive mean-field type control, IEEE Trans. Automat. Control 60 2015, 10, 2640–2649]. We use the risk-neutral model for which an optimal solution exists as a preliminary step. This is an extension of an initial control system in this type of problem, where an admissible controls set is convex. We establish necessary as well as sufficient optimality conditions for the risk-sensitive performance functional control problem. We illustrate the paper by giving two different examples for a linear quadratic system, and a numerical application as second example.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"1 - 18"},"PeriodicalIF":0.4,"publicationDate":"2020-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2024","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66996337","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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