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Random Operators and Stochastic Equations最新文献

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Stability of stochastic differential equations driven by multifractional Brownian motion 多分数布朗运动驱动的随机微分方程的稳定性
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-04-02 DOI: 10.1515/rose-2021-2055
Oussama El Barrimi, Y. Ouknine
{"title":"Stability of stochastic differential equations driven by multifractional Brownian motion","authors":"Oussama El Barrimi, Y. Ouknine","doi":"10.1515/rose-2021-2055","DOIUrl":"https://doi.org/10.1515/rose-2021-2055","url":null,"abstract":"Abstract Our aim in this paper is to establish some strong stability results for solutions of stochastic differential equations driven by a Riemann–Liouville multifractional Brownian motion. The latter is defined as a Gaussian non-stationary process with a Hurst parameter as a function of time. The results are obtained assuming that the pathwise uniqueness property holds and using Skorokhod’s selection theorem.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"87 - 96"},"PeriodicalIF":0.4,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2021-2055","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41492280","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
Existence results for a class of random delay integrodifferential equations 一类随机时滞积分微分方程的存在性结果
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-04-02 DOI: 10.1515/rose-2021-2054
Amadou Diop, M. Diop, K. Ezzinbi
{"title":"Existence results for a class of random delay integrodifferential equations","authors":"Amadou Diop, M. Diop, K. Ezzinbi","doi":"10.1515/rose-2021-2054","DOIUrl":"https://doi.org/10.1515/rose-2021-2054","url":null,"abstract":"Abstract In this paper, we consider a class of random partial integro-differential equations with unbounded delay. Existence of mild solutions are investigated by using a random fixed point theorem with a stochastic domain combined with Schauder’s fixed point theorem and Grimmer’s resolvent operator theory. The results are obtained under Carathéodory conditions. Finally, an example is provided to illustrate our results.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"79 - 86"},"PeriodicalIF":0.4,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2021-2054","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47793120","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: 3
Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients 两个相互独立的非Lipschitz系数分数布朗运动驱动的预期BSDE
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-02-02 DOI: 10.1515/rose-2020-2051
Sadibou Aidara, Yaya Sagna
{"title":"Anticipated BSDEs driven by two mutually independent fractional Brownian motions with non-Lipschitz coefficients","authors":"Sadibou Aidara, Yaya Sagna","doi":"10.1515/rose-2020-2051","DOIUrl":"https://doi.org/10.1515/rose-2020-2051","url":null,"abstract":"Abstract This paper deals with a class of anticipated backward stochastic differential equations driven by two mutually independent fractional Brownian motions. We essentially establish the existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout the paper is the divergence-type integral.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"27 - 39"},"PeriodicalIF":0.4,"publicationDate":"2021-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2051","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49154086","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: 1
Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution 制度转换金融市场下的连续时间均值方差投资选择:时间一致解
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-01-21 DOI: 10.1515/rose-2020-2050
I. Alia, F. Chighoub
{"title":"Continuous-time mean-variance portfolio selection with regime-switching financial market: Time-consistent solution","authors":"I. Alia, F. Chighoub","doi":"10.1515/rose-2020-2050","DOIUrl":"https://doi.org/10.1515/rose-2020-2050","url":null,"abstract":"Abstract This paper studies optimal time-consistent strategies for the mean-variance portfolio selection problem. Especially, we assume that the price processes of risky stocks are described by regime-switching SDEs. We consider a Markov-modulated state-dependent risk aversion and we formulate the problem in the game theoretic framework. Then, by solving a flow of forward-backward stochastic differential equations, an explicit representation as well as uniqueness results of an equilibrium solution are obtained.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"11 - 25"},"PeriodicalIF":0.4,"publicationDate":"2021-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2050","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47120980","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: 1
Probabilistic contraction under a control function 控制函数下的概率收缩
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-01-16 DOI: 10.1515/rose-2020-2049
B. Choudhury, Vandana Tiwari, T. Som, P. Saha
{"title":"Probabilistic contraction under a control function","authors":"B. Choudhury, Vandana Tiwari, T. Som, P. Saha","doi":"10.1515/rose-2020-2049","DOIUrl":"https://doi.org/10.1515/rose-2020-2049","url":null,"abstract":"Abstract Probabilistic metric spaces are metric structures having uncertainty built within their geometry, which has made them into an appropriate context for modelling many real life problems. Theoretical studies on these structures have also appeared extensively. This paper is intended for some development of fixed point theory in probabilistic metric spaces, which is an active area of contemporary research. We define a new contraction mapping in such spaces and show that the contraction has a unique fixed point if such spaces are G-complete with an arbitrary choice of a continuous t-norm. With a minimum t-norm, the result is further extended in any complete probabilistic metric space. The contraction is defined with the help of a control function which is different from several other control functions used in probabilistic fixed point theory by other authors. The methodology of the proof is new. An illustrative example is given. The present work is a part of probabilistic analysis.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"1 - 10"},"PeriodicalIF":0.4,"publicationDate":"2021-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2049","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41524482","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
Stability and prevalence of McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients 具有非Lipschitz系数的McKean–Vlasov随机微分方程的稳定性和普遍性
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2021-01-09 DOI: 10.1515/rose-2021-2053
Mohamed Amine Mezerdi, N. Khelfallah
{"title":"Stability and prevalence of McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients","authors":"Mohamed Amine Mezerdi, N. Khelfallah","doi":"10.1515/rose-2021-2053","DOIUrl":"https://doi.org/10.1515/rose-2021-2053","url":null,"abstract":"Abstract We consider various approximation properties for systems driven by a McKean–Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations is stable with respect to small perturbation of initial conditions, parameters and driving processes. Moreover, the unique strong solutions may be constructed by an effective approximation procedure. Finally, we show that the set of bounded uniformly continuous coefficients for which the corresponding MVSDE have a unique strong solution is a set of second category in the sense of Baire.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"29 1","pages":"67 - 78"},"PeriodicalIF":0.4,"publicationDate":"2021-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2021-2053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46579573","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: 1
Frontmatter Frontmatter
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2020-12-01 DOI: 10.1515/rose-2020-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/rose-2020-frontmatter4","DOIUrl":"https://doi.org/10.1515/rose-2020-frontmatter4","url":null,"abstract":"","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-frontmatter4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47079683","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
Predictable solution for reflected BSDEs when the obstacle is not right-continuous 当障碍物不是正确连续时，反射BSDE的可预测解决方案
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2020-11-07 DOI: 10.1515/rose-2020-2045
M. Marzougue, M. El Otmani
{"title":"Predictable solution for reflected BSDEs when the obstacle is not right-continuous","authors":"M. Marzougue, M. El Otmani","doi":"10.1515/rose-2020-2045","DOIUrl":"https://doi.org/10.1515/rose-2020-2045","url":null,"abstract":"Abstract In the present paper, we consider reflected backward stochastic differential equations when the reflecting obstacle is not necessarily right-continuous in a general filtration that supports a one-dimensional Brownian motion and an independent Poisson random measure. We prove the existence and uniqueness of a predictable solution for such equations under the stochastic Lipschitz coefficient by using the predictable Mertens decomposition.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"269 - 279"},"PeriodicalIF":0.4,"publicationDate":"2020-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2045","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49496266","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: 5
Stability of functionals of perturbed Markov chains under the condition of uniform minorization 一致二次化条件下扰动Markov链泛函的稳定性
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2020-11-07 DOI: 10.1515/rose-2020-2043
V. Golomoziy
{"title":"Stability of functionals of perturbed Markov chains under the condition of uniform minorization","authors":"V. Golomoziy","doi":"10.1515/rose-2020-2043","DOIUrl":"https://doi.org/10.1515/rose-2020-2043","url":null,"abstract":"Abstract In this paper, we investigate the stability of functionals and trajectories of two different, independent, time-inhomogeneous, discrete-time Markov chains on a general state space. We obtain various stability estimates such as an estimate for a difference in expectations of functionals, L 2 {L_{2}} stability, and a probability of large deviations. The key condition that is used is the minorization condition on the whole space. We consider different limitations on the functional and on the proximity of two chains. We use the coupling method as a primary technique in our proofs.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"237 - 251"},"PeriodicalIF":0.4,"publicationDate":"2020-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43690609","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
Harnack-type inequality for linear fractional stochastic equations 线性分式随机方程的Harnack型不等式
IF 0.4
Random Operators and Stochastic Equations Pub Date : 2020-11-07 DOI: 10.1515/rose-2020-2046
B. Boufoussi, S. Mouchtabih
{"title":"Harnack-type inequality for linear fractional stochastic equations","authors":"B. Boufoussi, S. Mouchtabih","doi":"10.1515/rose-2020-2046","DOIUrl":"https://doi.org/10.1515/rose-2020-2046","url":null,"abstract":"Abstract Using the coupling method and Girsanov theorem, we prove a Harnack-type inequality for a stochastic differential equation with non-Lipschitz drift and driven by a fractional Brownian motion with Hurst parameter H < 1 2 {H<frac{1}{2}} . We also investigate this inequality for a stochastic differential equation driven by an additive fractional Brownian sheet.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":"28 1","pages":"281 - 290"},"PeriodicalIF":0.4,"publicationDate":"2020-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/rose-2020-2046","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46352523","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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