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Quasi-sure analysis of two-parameter stochastic differential equations 双参数随机微分方程的准确定分析
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290019212
Jiagang Ren, Xicheng Zhang
{"title":"Quasi-sure analysis of two-parameter stochastic differential equations","authors":"Jiagang Ren, Xicheng Zhang","doi":"10.1080/10451120290019212","DOIUrl":"https://doi.org/10.1080/10451120290019212","url":null,"abstract":"We prove a Stroock-Varadhan type quasi-sure limit theorem for stochastic differential equations in the plane.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124194893","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: 4
A multidimensional central limit theorem for random walks on hypergroups 超群上随机游走的多维中心极限定理
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120212872
L. Gallardo
{"title":"A multidimensional central limit theorem for random walks on hypergroups","authors":"L. Gallardo","doi":"10.1080/10451120212872","DOIUrl":"https://doi.org/10.1080/10451120212872","url":null,"abstract":"Random walks on a product hypergroup of classical one-dimensional hypergroups are d -dimensional Markov chains which have a conditional increment with an asymptotically constant covariance matrix. We use this property and a central limit theorem for martingale differences, to show that such random walks suitably normalized converge to a standard Gaussian law N (0, o ) in R d with a covariance matrix o which is explicitly determined.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"2015 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127256781","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
Cahn-Hilliard stochastic equation: Strict positivity of the density Cahn-Hilliard随机方程:密度的严格正性
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290019195
C. Cardon-Weber
{"title":"Cahn-Hilliard stochastic equation: Strict positivity of the density","authors":"C. Cardon-Weber","doi":"10.1080/10451120290019195","DOIUrl":"https://doi.org/10.1080/10451120290019195","url":null,"abstract":"This paper deals with the Cahn-Hilliard stochastic equation driven by a space-time white noise with a non-linear diffusion coefficient. Using new lower estimate of the kernel, we prove the \"local\" existence of the density without non-degeneracy condition in a case of Hölder continuous trajectories, and we show that the density of any vector is lower bounded by a strictly positive continuous function under a non-degeneracy condition.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122264728","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: 23
On a general result for backward stochastic differential equations 关于倒向随机微分方程的一般结果
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290010923
M. Hassani, Y. Ouknine
{"title":"On a general result for backward stochastic differential equations","authors":"M. Hassani, Y. Ouknine","doi":"10.1080/10451120290010923","DOIUrl":"https://doi.org/10.1080/10451120290010923","url":null,"abstract":"The existence of the solution of a general infinite dimensional backward stochastic differential equation is discussed. In our setting, we generalize many works concerning the existence problem (by a new approach).","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132376732","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: 14
On a problem of optimal harvesting from a stochastic system with a jump component 具有跳跃分量的随机系统的最优收获问题
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000025970
C. Makasu
{"title":"On a problem of optimal harvesting from a stochastic system with a jump component","authors":"C. Makasu","doi":"10.1080/1045112021000025970","DOIUrl":"https://doi.org/10.1080/1045112021000025970","url":null,"abstract":"In this paper, we study a problem of optimal harvesting from a stochastic system modeled by a geometric Lévy process. A verification theorem of the variational inequality type is also given and proved. The paper has been motivated by I. Elsanosi et al. [Stochastics Stochastics Rep. (2000)], where the authors considered an optimal harvesting problem with price dynamics following a stochastic differential delay equation.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130373988","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
Quantitative approximation of certain stochastic integrals 若干随机积分的定量逼近
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000025934
S. Geiss
{"title":"Quantitative approximation of certain stochastic integrals","authors":"S. Geiss","doi":"10.1080/1045112021000025934","DOIUrl":"https://doi.org/10.1080/1045112021000025934","url":null,"abstract":"We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133809777","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: 55
Optimal stopping problems with discontinous reward: Regularity of the value function and viscosity solutions 具有不连续奖励的最优停止问题:值函数的规律性和粘性解
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290008557
Bruno Bassan, Claudia Ceci
{"title":"Optimal stopping problems with discontinous reward: Regularity of the value function and viscosity solutions","authors":"Bruno Bassan, Claudia Ceci","doi":"10.1080/10451120290008557","DOIUrl":"https://doi.org/10.1080/10451120290008557","url":null,"abstract":"We study optimal stopping problems for diffusion processes with discontinuous reward function. We give some results about the regularity of the value function and we show that, under suitable mild conditions on the underlying process, it has the same regularity of the reward function, namely, it is lower (respectively: upper) semicontinuous if the reward function is. The proofs for the two cases are quite different, and the upper semicontinuous case requires stronger conditions. Finally, we show that, in the case of lower semicontinuous reward, under suitable conditions the value function is a (discontinuous) viscosity solution of the associated variational inequalities.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133716340","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: 20
A large deviation principle with queueing applications 排队应用程序的大偏差原则
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120212871
Ayalvadi J. Ganesh, N. O’Connell
{"title":"A large deviation principle with queueing applications","authors":"Ayalvadi J. Ganesh, N. O’Connell","doi":"10.1080/10451120212871","DOIUrl":"https://doi.org/10.1080/10451120212871","url":null,"abstract":"In this paper, we present a large deviation principle for partial sums processes indexed by the half line, which is particularly suited to queueing applications. The large deviation principle is established in a topology that is finer than the topology of uniform convergence on compacts and in which the queueing map is continuous. Consequently, a large deviation principle for steady-state queue lengths can be obtained immediately via the contraction principle.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125251939","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: 46
Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs 具有跨期替代和交易成本的lsamvy市场中的投资组合优化
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/1045112021000037382
F. Benth, K. Karlsen, Kristin Reikvam
{"title":"Portfolio optimization in a Lévy market with intertemporal substitution and transaction costs","authors":"F. Benth, K. Karlsen, Kristin Reikvam","doi":"10.1080/1045112021000037382","DOIUrl":"https://doi.org/10.1080/1045112021000037382","url":null,"abstract":"We investigate an infinite horizon investment-consumption model in which a single agent consumes and distributes her wealth between a risk-free asset (bank account) and several risky assets (stocks) whose prices are governed by Lévy (jump-diffusion) processes. We suppose that transactions between the assets incur a transaction cost proportional to the size of the transaction. The problem is to maximize the total utility of consumption under Hindy-Huang-Kreps intertemporal preferences. This portfolio optimisation problem is formulated as a singular stochastic control problem and is solved using dynamic programming and the theory of viscosity solutions. The associated dynamic programming equation is a second order degenerate elliptic integro-differential variational inequality subject to a state constraint boundary condition. The main result is a characterization of the value function as the unique constrained viscosity solution of the dynamic programming equation. Emphasis is put on providing a framework that allows for a general class of Lévy processes. Owing to the complexity of our investment-consumption model, it is not possible to derive closed form solutions for the value function. Hence, the optimal policies cannot be obtained in closed form from the first order conditions for the dynamic programming equation. Therefore, we have to resort to numerical methods for computing the value function as well as the associated optimal policies. In view of the viscosity solution theory, the analysis found in this paper will ensure the convergence of a large class of numerical methods for the investment-consumption model in question.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114504059","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: 50
Generalized calculus and sdes with non regular drift 广义微积分与不规则漂移边
Stochastics and Stochastic Reports Pub Date : 2002-01-01 DOI: 10.1080/10451120290008548
F. Flandoli, F. Russo
{"title":"Generalized calculus and sdes with non regular drift","authors":"F. Flandoli, F. Russo","doi":"10.1080/10451120290008548","DOIUrl":"https://doi.org/10.1080/10451120290008548","url":null,"abstract":"A new approach to uniqueness and regular dependence on parameters for stochastic equations with non regular drift is presented. It is based on the generalized stochastic calculus developed in a recent paper by the authors.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"175 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124250438","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: 10
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