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Stochastics-An International Journal of Probability and Stochastic Processes最新文献

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A note on convex ordering for stable stochastic integrals 稳定随机积分的凸排序问题
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-04-10 DOI: 10.1080/17442508.2014.989528
A. Joulin, Solym Mawaki Manou-Abi
{"title":"A note on convex ordering for stable stochastic integrals","authors":"A. Joulin, Solym Mawaki Manou-Abi","doi":"10.1080/17442508.2014.989528","DOIUrl":"https://doi.org/10.1080/17442508.2014.989528","url":null,"abstract":"We establish a convex ordering between stochastic integrals driven by strictly α-stable processes with index α ∈ (1,2). Our approach is based on the forward–backward stochastic calculus for martingales together with a suitable decomposition of stable stochastic integrals.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84043971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On estimation of the extended Orey index for Gaussian processes 高斯过程扩展Orey指数的估计
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-04-09 DOI: 10.1080/17442508.2014.989527
K. Kubilius
{"title":"On estimation of the extended Orey index for Gaussian processes","authors":"K. Kubilius","doi":"10.1080/17442508.2014.989527","DOIUrl":"https://doi.org/10.1080/17442508.2014.989527","url":null,"abstract":"Orey suggested the definition of an index for a Gaussian process with stationary increments which determines various properties of the sample paths of this process. We provide an extension of the definition of the Orey index towards a second-order stochastic process which may not have stationary increments and estimate the Orey index towards a Gaussian process from discrete observations of its sample paths.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85770710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Asymptotic results for empirical means of independent geometric distributed random variables 独立几何分布随机变量经验均值的渐近结果
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.942307
C. Macci, B. Pacchiarotti
{"title":"Asymptotic results for empirical means of independent geometric distributed random variables","authors":"C. Macci, B. Pacchiarotti","doi":"10.1080/17442508.2014.942307","DOIUrl":"https://doi.org/10.1080/17442508.2014.942307","url":null,"abstract":"We consider independent geometric distributed random variables which satisfy suitable hypotheses. We study large and moderate deviations for their empirical means, and we illustrate applications of the large deviation results for the weak record values of i.i.d. discrete random variables.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89825969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Some preliminary results on conditionally ψ-mixing sequences of random variables 关于随机变量有条件的ψ-混合序列的一些初步结果
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.944913
D. Yuan, Shunjing Li, B. Tao
{"title":"Some preliminary results on conditionally ψ-mixing sequences of random variables","authors":"D. Yuan, Shunjing Li, B. Tao","doi":"10.1080/17442508.2014.944913","DOIUrl":"https://doi.org/10.1080/17442508.2014.944913","url":null,"abstract":"From the ordinary notion of -mixing for a sequence of random variables, a new concept called conditionally -mixing is proposed. That conditionally -mixing neither implies nor is implied by -mixing is illustrated by examples. Certain criteria for checking conditionally -mixing property as well as basic properties are derived, and several conditional covariance inequalities are obtained. By means of these properties and inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90214012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Entry and exit decisions with linear costs under uncertainty 不确定条件下具有线性成本的进入和退出决策
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.939976
Yongchao Zhang
{"title":"Entry and exit decisions with linear costs under uncertainty","authors":"Yongchao Zhang","doi":"10.1080/17442508.2014.939976","DOIUrl":"https://doi.org/10.1080/17442508.2014.939976","url":null,"abstract":"From the viewpoint of stochastic programming, we rigorously analyse entry and exit decisions of a project which were proposed by Dixit [A. Dixit, Entry and exit decisions under uncertainty, J. Polit. Econ. 97 (1989), pp. 620–638]. In this article, instead of assuming that the costs are constant in classical research, we assume that they are linear with respect to the price of the commodity produced by the project. Under this assumption, we obtain a condition which guarantees that investing in the project is worthless; besides, the project may be terminated when the commodity price is greater than a certain value. In contrast, there are no such results provided that the costs are constant. Moreover, we provide an explicit solution of entry and exit decisions if the project is worthy to be invested in.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78952609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities 利用经验分布和集中不等式逼近平均成本马尔可夫决策过程
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.939979
F. Dufour, T. Prieto-Rumeau
{"title":"Approximation of average cost Markov decision processes using empirical distributions and concentration inequalities","authors":"F. Dufour, T. Prieto-Rumeau","doi":"10.1080/17442508.2014.939979","DOIUrl":"https://doi.org/10.1080/17442508.2014.939979","url":null,"abstract":"We consider a discrete-time Markov decision process with Borel state and action spaces, and possibly unbounded cost function. We assume that the Markov transition kernel is absolutely continuous with respect to some probability measure . By replacing this probability measure with its empirical distribution for a sample of size n, we obtain a finite state space control problem, which is used to provide an approximation of the optimal value and an optimal policy of the original control model. We impose Lipschitz continuity properties on the control model and its associated density functions. We measure the accuracy of the approximation of the optimal value and an optimal policy by means of a non-asymptotic concentration inequality based on the 1-Wasserstein distance between and . Obtaining numerically the solution of the approximating control model is discussed and an application to an inventory management problem is presented.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83987273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 29
On the rate of convergence in the strong law of large numbers for martingales 关于鞅强大数定律的收敛速度
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.938075
Y. Miao, Guangyu Yang, G. Stoica
{"title":"On the rate of convergence in the strong law of large numbers for martingales","authors":"Y. Miao, Guangyu Yang, G. Stoica","doi":"10.1080/17442508.2014.938075","DOIUrl":"https://doi.org/10.1080/17442508.2014.938075","url":null,"abstract":"The aim of this note is to establish the Baum–Katz type rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759–763; Baum–Katz–Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489–1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910–913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77194501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Complete qth moment convergence of weighted sums for arrays of rowwise negatively associated random variables 完成行负相关随机变量数组加权和的第q阶收敛
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.939978
M. Guo, Dongjin Zhu, Yong Ren
{"title":"Complete qth moment convergence of weighted sums for arrays of rowwise negatively associated random variables","authors":"M. Guo, Dongjin Zhu, Yong Ren","doi":"10.1080/17442508.2014.939978","DOIUrl":"https://doi.org/10.1080/17442508.2014.939978","url":null,"abstract":"In this paper, the complete qth moment convergence of weighted sums for arrays of rowwise negatively associated (NA) random variables is investigated. By using moment inequality and truncation methods, some general results on complete qth moment convergence of weighted sums for arrays of rowwise NA random variables are obtained. As their applications, we not only generalize and extend the corresponding results of Baek et al. [On the complete convergence of weighted sums for arrays of negatively associated variables, J. Korean Stat. Soc. 37 (2008), pp. 73–80], Liang [Complete convergence for weighted sums of negatively associated random variables, Stat. Probab. Lett. 48 (2000), pp. 317–325 and Liang et al. [Complete moment convergence for sums of negatively associated random variables, Acta Math. Sin. English Ser. 26 (2010), pp. 419–432], but also greatly simplify their proofs.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73007282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Complete moment convergence of pairwise NQD random variables 成对NQD随机变量的完全矩收敛性
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-03-04 DOI: 10.1080/17442508.2014.939975
Wenzhi Yang, Shuhe Hu
{"title":"Complete moment convergence of pairwise NQD random variables","authors":"Wenzhi Yang, Shuhe Hu","doi":"10.1080/17442508.2014.939975","DOIUrl":"https://doi.org/10.1080/17442508.2014.939975","url":null,"abstract":"It is known that the dependence structure of pairwise negative quadrant dependent (NQD) random variables is weaker than those of negatively associated random variables and negatively orthant dependent random variables. In this article, we investigate the moving average process which is based on the pairwise NQD random variables. The complete moment convergence and the integrability of the supremum are presented for this moving average process. The results imply complete convergence and the Marcinkiewicz–Zygmund-type strong law of large numbers for pairwise NQD sequences.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88375822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 17
Worst-case portfolio optimization with proportional transaction costs 交易成本成比例的最坏情况投资组合优化
IF 0.9 4区 数学
Stochastics-An International Journal of Probability and Stochastic Processes Pub Date : 2015-02-20 DOI: 10.1080/17442508.2014.991325
Christoph Belak, Olaf Menkens, Jörn Sass
{"title":"Worst-case portfolio optimization with proportional transaction costs","authors":"Christoph Belak, Olaf Menkens, Jörn Sass","doi":"10.1080/17442508.2014.991325","DOIUrl":"https://doi.org/10.1080/17442508.2014.991325","url":null,"abstract":"We study optimal asset allocation in a crash-threatened financial market with proportional transaction costs. The market is assumed to be either in a normal state, in which the risky asset follows a geometric Brownian motion, or in a crash state, in which the price of the risky asset can suddenly drop by a certain relative amount. We only assume the maximum number and the maximum relative size of the crashes to be given and do not make any assumptions about their distributions. For every investment strategy, we identify the worst-case scenario in the sense that the expected utility of terminal wealth is minimized. The objective is then to determine the investment strategy which yields the highest expected utility in its worst-case scenario. We solve the problem for utility functions with constant relative risk aversion using a stochastic control approach. We characterize the value function as the unique viscosity solution of a second-order nonlinear partial differential equation. The optimal strategies are characterized by time-dependent free boundaries which we compute numerically. The numerical examples suggest that it is not optimal to invest any wealth in the risky asset close to the investment horizon, while a long position in the risky asset is optimal if the remaining investment period is sufficiently large.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2015-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89086770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 13
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