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Random Operators and Stochastic Equations最新文献

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Radonification of a cylindrical Lévy process 圆柱形lsamvy过程的辐射化
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-05-16 DOI: 10.1515/rose-2023-2010
A. E. Alvarado-Solano
{"title":"Radonification of a cylindrical Lévy process","authors":"A. E. Alvarado-Solano","doi":"10.1515/rose-2023-2010","DOIUrl":"https://doi.org/10.1515/rose-2023-2010","url":null,"abstract":"Abstract In this work, we present a direct proof about radonification of a cylindrical Lévy process. The radonification technique has been very useful to define a genuine stochastic process starting from a cylindrical process; this is possible thanks to the Hilbert–Schmidt operators. With this work, we want to propose a self-contained simple proof to those who are not familiar with this method and also present our result which is to apply the radonification method to the case of a cylindrical Lévy process.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"199 - 204"},"PeriodicalIF":0.4,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44605334","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}
引用次数: 0
Partial information maximum principle for optimal control problem with regime switching in the conditional mean-field model 条件平均场模型中状态切换最优控制问题的部分信息最大值原理
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-03-31 DOI: 10.1515/rose-2022-2094
Lazhar Tamer, Hani Ben Abdallah
{"title":"Partial information maximum principle for optimal control problem with regime switching in the conditional mean-field model","authors":"Lazhar Tamer, Hani Ben Abdallah","doi":"10.1515/rose-2022-2094","DOIUrl":"https://doi.org/10.1515/rose-2022-2094","url":null,"abstract":"Abstract This paper is concerned with a stochastic optimal control problem for a Markov regime switching in the conditional mean field model. Sufficient and necessary maximum principles for optimal control under partial information are obtained. Finally, we illustrate our result through a model which gives an explicit solution.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"103 - 115"},"PeriodicalIF":0.4,"publicationDate":"2023-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46266769","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}
引用次数: 0
Frontmatter 头版头条
Random Operators and Stochastic Equations Pub Date : 2023-03-01 DOI: 10.1515/rose-2023-frontmatter1
{"title":"Frontmatter","authors":"","doi":"10.1515/rose-2023-frontmatter1","DOIUrl":"https://doi.org/10.1515/rose-2023-frontmatter1","url":null,"abstract":"","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136271103","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}
引用次数: 0
Le Cam–Stratonovich–Boole theory for Itô diffusions Le Cam–Stratonovich–Itôdiffusions的布尔理论
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2004
J. Bishwal
{"title":"Le Cam–Stratonovich–Boole theory for Itô diffusions","authors":"J. Bishwal","doi":"10.1515/rose-2023-2004","DOIUrl":"https://doi.org/10.1515/rose-2023-2004","url":null,"abstract":"Abstract We connect the theory of local asymptotic normality (LAN) of Le Cam to Boole’s approximation of the Stratonovich stochastic integral by estimating the parameter in the nonlinear drift coefficient of an ergodic diffusion process satisfying a homogeneous Itô stochastic differential equation based on discretely spaced dense observations of the process. The asymptotic normality and local asymptotic minimaxity (in the Hajek–Le Cam sense) of approximate maximum likelihood estimators, approximate maximum probability estimators and approximate Bayes estimators based on Itô and Boole’s approximations of the continuous likelihood are obtained under an almost slowly increasing experimental design (ASIED) condition ( T n 6 / 7 → 0 {frac{T}{n^{6/7}}to 0} as T → ∞ {Ttoinfty} and n → ∞ {ntoinfty} , where T is the length of the observation time and n is the number of observations) through the weak convergence of the approximate likelihood ratio random fields. Among other things, the Bernstein–von Mises type theorems concerning the convergence of suitably normalized and centered approximate posterior distributions to normal distribution under the same design condition are proved. Asymptotic normality and asymptotic efficiency of the conditional least squares estimator under the same design condition are obtained as a by-product. The log-likelihood derivatives based on Itô approximations are martingales, but the log-likelihood derivatives based on Boole’s approximations are not martingales but weighted averages of forward and backward martingales. These new approximations have faster rate of convergence than the martingale approximations. The methods would have advantages over Euler and Milstein approximations for Monte Carlo simulations.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"153 - 176"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49364886","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}
引用次数: 0
The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero 包含零点局部时间的一维随机微分方程的截断Euler-Maruyama方法
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2003
Kamal Hiderah
{"title":"The truncated Euler–Maruyama method of one-dimensional stochastic differential equations involving the local time at point zero","authors":"Kamal Hiderah","doi":"10.1515/rose-2023-2003","DOIUrl":"https://doi.org/10.1515/rose-2023-2003","url":null,"abstract":"Abstract Recently, Mao developed a new explicit method, called the truncated Euler–Maruyama method for nonlinear SDEs, and established the strong convergence theory under the local Lipschitz condition plus the Khasminskii-type condition. The key aim of this paper is to establish the rate of strong convergence of the truncated Euler–Maruyama method for one-dimensional stochastic differential equations involving that the local time at point zero under the drift coefficient satisfies a one-sided Lipschitz condition and plus some additional conditions.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"141 - 152"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43115526","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}
引用次数: 0
A chaotic decomposition for the fractional Lebesgue–Pascal noise space 分数阶Lebesgue–Pascal噪声空间的混沌分解
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2005
A. Riahi
{"title":"A chaotic decomposition for the fractional Lebesgue–Pascal noise space","authors":"A. Riahi","doi":"10.1515/rose-2023-2005","DOIUrl":"https://doi.org/10.1515/rose-2023-2005","url":null,"abstract":"Abstract This paper is devoted to study the fractional Pascal noise functionals on compound configuration spaces with special emphasis on the chaotic decomposition of the Hilbert spaces of quadratic integrable functionals with respect to the correlation measure corresponding to the fractional Pascal measure in infinite dimensions.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"177 - 183"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49378668","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}
引用次数: 0
Risk process with mixture of tempered stable inverse subordinators: Analysis and synthesis 混合调和稳定逆从属项的风险过程：分析与综合
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2022-2096
T. Kadankova, Wing Chun Vincent Ng
{"title":"Risk process with mixture of tempered stable inverse subordinators: Analysis and synthesis","authors":"T. Kadankova, Wing Chun Vincent Ng","doi":"10.1515/rose-2022-2096","DOIUrl":"https://doi.org/10.1515/rose-2022-2096","url":null,"abstract":"Abstract We propose two fractional risk models, where the classical risk process is time-changed by the mixture of tempered stable inverse subordinators. We characterize the risk processes by deriving the marginal distributions and establish the moments and covariance structure. We study the main characteristics of these models such as ruin probability and time to ruin and illustrate the results with Monte Carlo simulations. The data suggest that the ruin time can be approximated by the inverse gaussian distribution and its generalizations.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"47 - 63"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46053245","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}
引用次数: 0
𝕃2-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration 具有弱单调性的多维广义BSDEs的𝕃2-solutions和一般滤波中的一般生长发生器
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2002
R. Belfadli, Tarik El Mellali, Imade Fakhouri, Y. Ouknine
{"title":"𝕃2-solutions of multidimensional generalized BSDEs with weak monotonicity and general growth generators in a general filtration","authors":"R. Belfadli, Tarik El Mellali, Imade Fakhouri, Y. Ouknine","doi":"10.1515/rose-2023-2002","DOIUrl":"https://doi.org/10.1515/rose-2023-2002","url":null,"abstract":"Abstract In this paper, we study multidimensional generalized backward stochastic differential equations (GBSDEs), in a general filtration supporting a Brownian motion and an independent Poisson random measure, whose generators are weakly monotone and satisfy a general growth condition with respect to the state variable y. We show that such GBSDEs admit a unique 𝕃 2 {mathbb{L}^{2}} -solution. The main tools and techniques used in the proofs are the a-priori-estimation, the convolution approach, the iteration, the truncation, and the Bihari inequality.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"117 - 139"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46753855","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}
引用次数: 0
Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise 广义Hermite过程(gHp)的Wiener积分。应用范围:具有高频噪声的SDEs
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2001
Atef Lechiheb
{"title":"Wiener integrals with respect to the generalized Hermite process (gHp). Applications: SDEs with gHp noise","authors":"Atef Lechiheb","doi":"10.1515/rose-2023-2001","DOIUrl":"https://doi.org/10.1515/rose-2023-2001","url":null,"abstract":"Abstract In this paper, we introduce Wiener integrals with respect to the generalized Hermite process and we prove a non-central limit theorem in which this integral appears as limit. As an application, we investigate the corresponding stochastic differential equations with the generalized Hermite process as a driving noise, we prove the existence and the uniqueness of the solution, and we give a generalization of the Hermite Ornstein–Uhlenbeck process and the Hermite-driving Vasicek process.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"87 - 102"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47341199","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}
引用次数: 0
Lp -solution for BSDEs driven by a Lévy process Lp-由Lévy过程驱动的BSDE的解决方案
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2023-02-28 DOI: 10.1515/rose-2023-2006
M. El Jamali
{"title":"Lp -solution for BSDEs driven by a Lévy process","authors":"M. El Jamali","doi":"10.1515/rose-2023-2006","DOIUrl":"https://doi.org/10.1515/rose-2023-2006","url":null,"abstract":"Abstract This paper deals with the problem of existence and uniqueness of 𝕃 p {mathbb{L}^{p}} -solutions for a backward stochastic differential equation in a filtration that supports Lévy processes with p ∈ ( 1 , 2 ) {pin(1,2)} . However, we will focus on when the data satisfy the appropriate integrability conditions and when the coefficient is Lipschitz.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"31 1","pages":"185 - 197"},"PeriodicalIF":0.4,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43627325","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}
引用次数: 0
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