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Uniqueness Result for the 2D Navier–Stokes Equation with Additive Noise 具有加性噪声的二维Navier-Stokes方程的唯一性结果
Stochastics and Stochastic Reports Pub Date : 2003-12-01 DOI: 10.1080/10451120310001644485
B. Ferrario
{"title":"Uniqueness Result for the 2D Navier–Stokes Equation with Additive Noise","authors":"B. Ferrario","doi":"10.1080/10451120310001644485","DOIUrl":"https://doi.org/10.1080/10451120310001644485","url":null,"abstract":"A bidimensional stochastic Navier–Stokes equation with an additive noise is considered. Known results on existence of generalized solutions are reviewed, in order to state an existence result in the most complete form. For this kind of generalized solutions, pathwise uniqueness is proven.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127601943","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: 12
Stochastic variational inequalities and optimal stopping: applications to the robustness of the portfolio/consumption processes 随机变分不等式和最优停止:投资组合/消费过程稳健性的应用
Stochastics and Stochastic Reports Pub Date : 2003-12-01 DOI: 10.1080/10451120310001641135
Akaki Danelia, B. Dochviri, M. Shashiashvili
{"title":"Stochastic variational inequalities and optimal stopping: applications to the robustness of the portfolio/consumption processes","authors":"Akaki Danelia, B. Dochviri, M. Shashiashvili","doi":"10.1080/10451120310001641135","DOIUrl":"https://doi.org/10.1080/10451120310001641135","url":null,"abstract":"We give a new characterization of the Snell envelope of a given process as the unique solution of the stochastic variational inequality (SVI) in this article. This approach leads to several a priori estimates for the Snell envelopes and their components. The valuation for American Contingent Claims (ACC) in general financial market model is considered as an application. The robustness of the optimal portfolio/consumption processes with respect to the payoff function is established.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130973848","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
Cramér's asymptotics in systems with fast and slow motions 具有快慢运动系统的cramsamr渐近性
Stochastics and Stochastic Reports Pub Date : 2003-10-01 DOI: 10.1080/1045112031000155669
V. Bakhtin
{"title":"Cramér's asymptotics in systems with fast and slow motions","authors":"V. Bakhtin","doi":"10.1080/1045112031000155669","DOIUrl":"https://doi.org/10.1080/1045112031000155669","url":null,"abstract":"This paper is devoted to the averaging principle for stochastic systems with slow and intermixing fast motions. Here we (i) prove the existence of the Cramér type asymptotics for the probabilities of large deviations from an averaged motion, which implies the central limit theorem, and (ii) develop an analytic procedure for computation of this asymptotics. We use general apparatus of superregular perturbations of fiber ergodic semigroups to investigate two systems in the same way. The first of them is a cascade in which slow motions are determined by a vector field depending both on slow and fast variables, and fast motions compose a Markov chain depending on the slow variable. The second is a process defined by a system of two stochastic differential equations.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115706174","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: 9
A predictable decomposition in an infinite assets model with jumps. Application to hedging and optimal investment 具有跳跃的无限资产模型中的可预测分解。套期保值和最优投资的应用
Stochastics and Stochastic Reports Pub Date : 2003-10-01 DOI: 10.1080/104511203100001621237
H. Pham
{"title":"A predictable decomposition in an infinite assets model with jumps. Application to hedging and optimal investment","authors":"H. Pham","doi":"10.1080/104511203100001621237","DOIUrl":"https://doi.org/10.1080/104511203100001621237","url":null,"abstract":"Motivated by the theory of bond markets, we consider an infinite assets model driven by marked point process and Wiener process. The self-financed wealth processes are defined by using measure-valued strategies. Going further on the works of Bjork et al. [“Bond market structure in the presence of marked point processes”, Mathematical Finance, 7 (1997a) pp. 211–239; “Towards a general theory of bond markets”, Finance and Stochastics, 1 (1997b) pp. 141–174] who focus on the existence of martingale measures and market completeness questions, we study here the incompleteness case. Our main result is a predictable decomposition theorem for supermartingales in this infinite assets model context. The concept of approximate wealth processes is introduced, and we show in an example that the space of measure-valued strategies is not complete with respect to the semimartingale topology. As in the case of stock markets, one can then derive a dual representation of the super-replication cost and study the problem of utility maximization by duality methods.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123942458","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: 32
Penalization methods for reflecting stochastic differential equations with jumps 反映有跳跃的随机微分方程的惩罚方法
Stochastics and Stochastic Reports Pub Date : 2003-10-01 DOI: 10.1080/1045112031000155687
Weronika Łaukajtys, L. Slominski
{"title":"Penalization methods for reflecting stochastic differential equations with jumps","authors":"Weronika Łaukajtys, L. Slominski","doi":"10.1080/1045112031000155687","DOIUrl":"https://doi.org/10.1080/1045112031000155687","url":null,"abstract":"The problem of approximation of a solution to a reflecting stochastic differential equation (SDE) with jumps by a sequence of solutions to SDEs with penalization terms is considered. The approximating sequence is not relatively compact in the Skorokhod topology J 1 and so the methods of approximation based on the J 1-topology break down. In the paper, we prove our convergence results in the S-topology on the Skorokhod space D(R+, R d ) introduced recently by Jakubowski. The S-topology is weaker than J 1 but stronger than the Meyer-Zheng topology and shares many useful properties with J 1.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128957179","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: 28
Asymptotics of superregular perturbations of fiber ergodic semigroups 纤维遍历半群的超正则微扰渐近性
Stochastics and Stochastic Reports Pub Date : 2003-10-01 DOI: 10.1080/1045112031000155678
V. Bakhtin
{"title":"Asymptotics of superregular perturbations of fiber ergodic semigroups","authors":"V. Bakhtin","doi":"10.1080/1045112031000155678","DOIUrl":"https://doi.org/10.1080/1045112031000155678","url":null,"abstract":"In this paper, we investigate a semigroup of conditional expectation operators generated by a stochastic system with slow and intermixing fast motions, in which the slow motions have a speed of order ε. This semigroup, considered as perturbation of possess a number of unexpected properties; the most important of them is superregularity. First we study these properties. Then we construct an asymptotic expansion for the family by powers of ξ, ε, where ξ is a small complex parameter and F is a function of the slow variable. We reveal a new non-trivial phenomenon: each coefficient of the last expansion appears as a sum of four terms of different types. This expansion gives a powerful tool for proving some probability limit theorems for the slow motion behavior over the time periods of order ε -1.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131369168","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
The cone of positive harmonic functions for scale-invariant diffusions 尺度不变扩散的正调和函数锥
Stochastics and Stochastic Reports Pub Date : 2003-08-01 DOI: 10.1080/1045112031000120649
R. Dante DeBlassie
{"title":"The cone of positive harmonic functions for scale-invariant diffusions","authors":"R. Dante DeBlassie","doi":"10.1080/1045112031000120649","DOIUrl":"https://doi.org/10.1080/1045112031000120649","url":null,"abstract":"Consider a scale invariant diffusion whose state space is a closed cone in R d , minus the vertex. Then the process is either recurrent, transient to ∞ or transient to the vertex of the cone. In the latter case, the diffusion has finite lifetime (a.s.) and converges to the vertex at the lifetime. The Martin boundary consists of two points, and the corresponding minimal harmonic functions are of the form 1 and |x| α ψ(x/|x|).","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116514027","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
Ergodic Control of Partially Degenerate Diffusions in a Compact Domain 紧域上部分简并扩散的遍历控制
Stochastics and Stochastic Reports Pub Date : 2003-08-01 DOI: 10.1080/1045112031000070357
V. Borkar, M. K. Ghosh
{"title":"Ergodic Control of Partially Degenerate Diffusions in a Compact Domain","authors":"V. Borkar, M. K. Ghosh","doi":"10.1080/1045112031000070357","DOIUrl":"https://doi.org/10.1080/1045112031000070357","url":null,"abstract":"The problem of ergodic control of a reflecting diffusion in a compact domain is analysed under the condition of partial degeneracy, i.e. when its transition kernel after some time is absolutely continuous with respect to the Lebesgue measure on a part of the state space. Existence of a value function and a “martingale dynamic programming principle” are established by mapping the problem to a discrete time control problem. Implications for existence of optimal controls are derived.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"139 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131725272","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: 2
Optimal prediction of the ultimate maximum of Brownian motion 布朗运动最终最大值的最优预测
Stochastics and Stochastic Reports Pub Date : 2003-08-01 DOI: 10.1080/1045112031000118994
J. L. Pedersen
{"title":"Optimal prediction of the ultimate maximum of Brownian motion","authors":"J. L. Pedersen","doi":"10.1080/1045112031000118994","DOIUrl":"https://doi.org/10.1080/1045112031000118994","url":null,"abstract":"At time 0 start to observe a Brownian path. Based upon the information, which is continuously updated through the observation of the path, a stopping time is determined such that the path is as close as possible to its unknown ultimate maximum over a finite time interval. The closeness is measured by a q-mean or by a probability distance. This can be formulated as an optimal stopping problem. The method of proof relies upon a representation of a conditional expectation of the gain process and the principle of smooth fit (at a single point).","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":"84 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117142020","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: 47
Capacity expansion with exponential jump diffusion processes 具有指数跳跃扩散过程的容量扩展
Stochastics and Stochastic Reports Pub Date : 2003-08-01 DOI: 10.1080/1045112031000155696
Hui Wang
{"title":"Capacity expansion with exponential jump diffusion processes","authors":"Hui Wang","doi":"10.1080/1045112031000155696","DOIUrl":"https://doi.org/10.1080/1045112031000155696","url":null,"abstract":"This paper studies an irreversible capacity expansion problem where the industry demand is described by a double exponential jump diffusion process. Formally, we consider the following optimization problem over all adapted, non-decreasing process Here we understand X t as the cumulative capital investment up to time t (it is non-decreasing since the investment is assumed to be irreversible). is the exogenous industry demand process, which is modeled by a double exponential jump diffusion. The profit flow is assumed to have rate for some concave function H, while k denotes the cost of unit capital. The goal is choosing a capital investment strategy X so as to maximize the discounted overall profit, net the cost of investing. We explicitly solve the problem when H is assumed to be the Cobb–Douglas production function, that is, for some Throughout the paper, a slightly different (but essentially the same) optimization criterion is adopted, for the sake of technical convenience.","PeriodicalId":289792,"journal":{"name":"Stochastics and Stochastic Reports","volume":" 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113949344","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: 18
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