Pub Date : 2014-03-04DOI: 10.1080/17442508.2013.775289
A. Shen, R. Wu
In this article, the complete convergence for sequences of asymptotically almost negatively associated (AANA) random variables is studied. As applications, the Baum–Katz-type theorem, Hsu–Robbins-type theorem and Marcinkiewicz–Zygmund strong law of large numbers for sequences of AANA random variables are obtained.
{"title":"Strong convergence for sequences of asymptotically almost negatively associated random variables","authors":"A. Shen, R. Wu","doi":"10.1080/17442508.2013.775289","DOIUrl":"https://doi.org/10.1080/17442508.2013.775289","url":null,"abstract":"In this article, the complete convergence for sequences of asymptotically almost negatively associated (AANA) random variables is studied. As applications, the Baum–Katz-type theorem, Hsu–Robbins-type theorem and Marcinkiewicz–Zygmund strong law of large numbers for sequences of AANA random variables are obtained.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"12 1","pages":"291 - 303"},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86933898","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}
Pub Date : 2014-03-04DOI: 10.1080/17442508.2013.775288
M. Pronk
In this article, we give an alternative example of a Skorohod integrable process for which a truncated version is not Skorohod integrable. We also give a relationship with the spaces .
{"title":"A note on the truncated Skorohod integral process","authors":"M. Pronk","doi":"10.1080/17442508.2013.775288","DOIUrl":"https://doi.org/10.1080/17442508.2013.775288","url":null,"abstract":"In this article, we give an alternative example of a Skorohod integrable process for which a truncated version is not Skorohod integrable. We also give a relationship with the spaces .","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"4 1","pages":"285 - 290"},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85291196","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}
Pub Date : 2014-03-04DOI: 10.1080/17442508.2013.797422
M. Pemy
We consider a finite time horizon optimal stopping of a regime-switching Lévy process. We prove that the value function of the optimal stopping problem can be characterized as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman variational inequalities.
{"title":"Optimal stopping of Markov switching Lévy processes","authors":"M. Pemy","doi":"10.1080/17442508.2013.797422","DOIUrl":"https://doi.org/10.1080/17442508.2013.797422","url":null,"abstract":"We consider a finite time horizon optimal stopping of a regime-switching Lévy process. We prove that the value function of the optimal stopping problem can be characterized as the unique viscosity solution of the associated Hamilton–Jacobi–Bellman variational inequalities.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"191 1","pages":"341 - 369"},"PeriodicalIF":0.9,"publicationDate":"2014-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73347292","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}
Pub Date : 2014-02-12DOI: 10.1080/17442508.2015.1012081
Almut E. D. Veraart
This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also, two methods for parameterizing the weight functions in the MA representation are presented: one method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalized Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.
{"title":"Stationary and multi-self-similar random fields with stochastic volatility","authors":"Almut E. D. Veraart","doi":"10.1080/17442508.2015.1012081","DOIUrl":"https://doi.org/10.1080/17442508.2015.1012081","url":null,"abstract":"This paper introduces stationary and multi-self-similar random fields which account for stochastic volatility and have type G marginal law. The stationary random fields are constructed using volatility modulated mixed moving average (MA) fields and their probabilistic properties are discussed. Also, two methods for parameterizing the weight functions in the MA representation are presented: one method is based on Fourier techniques and aims at reproducing a given correlation structure, the other method is based on ideas from stochastic partial differential equations. Moreover, using a generalized Lamperti transform we construct volatility modulated multi-self-similar random fields which have type G distribution.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"32 1","pages":"848 - 870"},"PeriodicalIF":0.9,"publicationDate":"2014-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84762639","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2012.755625
S. Minkevičius
The paper is devoted to the analysis of queueing systems in the context of the network and communication theory. We investigate a theorem on the law of the iterated logarithm for a queue of jobs in a multiserver open queueing network under heavy traffic conditions.
{"title":"On the law of the iterated logarithm in multiserver open queueing networks","authors":"S. Minkevičius","doi":"10.1080/17442508.2012.755625","DOIUrl":"https://doi.org/10.1080/17442508.2012.755625","url":null,"abstract":"The paper is devoted to the analysis of queueing systems in the context of the network and communication theory. We investigate a theorem on the law of the iterated logarithm for a queue of jobs in a multiserver open queueing network under heavy traffic conditions.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"39 1","pages":"46 - 59"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75325176","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2012.748057
Xiaoyong Xiao, H. Yin
Suppose that the moving average process is based on a doubly infinite sequence of identically distributed and dependent random variables with zero mean and finite variance and that the sequence of coefficients is absolutely summable. Under suitable conditions of dependence, we show the precise rates in the law of logarithm of a kind of weighted infinite series for the first moment of the partial sums of the moving average process. This generalizes the common law of logarithm with the square root of logarithm to that with any positive power of logarithm. Moreover, we provide another law of logarithm as a supplement.
{"title":"Moment convergence rates in the law of logarithm for moving average process under dependence","authors":"Xiaoyong Xiao, H. Yin","doi":"10.1080/17442508.2012.748057","DOIUrl":"https://doi.org/10.1080/17442508.2012.748057","url":null,"abstract":"Suppose that the moving average process is based on a doubly infinite sequence of identically distributed and dependent random variables with zero mean and finite variance and that the sequence of coefficients is absolutely summable. Under suitable conditions of dependence, we show the precise rates in the law of logarithm of a kind of weighted infinite series for the first moment of the partial sums of the moving average process. This generalizes the common law of logarithm with the square root of logarithm to that with any positive power of logarithm. Moreover, we provide another law of logarithm as a supplement.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"86 1","pages":"1 - 15"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83339159","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2012.756489
Z. Tan, Linjun Tang
In this note, the asymptotic relation between the maximum of a continuous strongly dependent stationary Gaussian process and the maximum of this process sampled at discrete time points is studied. It is shown that these two extreme values are asymptotically totally dependent no matter what the grid of the discrete time points is.
{"title":"The dependence of extreme values of discrete and continuous time strongly dependent Gaussian processes","authors":"Z. Tan, Linjun Tang","doi":"10.1080/17442508.2012.756489","DOIUrl":"https://doi.org/10.1080/17442508.2012.756489","url":null,"abstract":"In this note, the asymptotic relation between the maximum of a continuous strongly dependent stationary Gaussian process and the maximum of this process sampled at discrete time points is studied. It is shown that these two extreme values are asymptotically totally dependent no matter what the grid of the discrete time points is.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"32 1","pages":"60 - 69"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90511063","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2013.763807
Jun Xian, Song-Hua Li
In this paper, combining stochastic processes with shift-invariant spaces, we introduce shift-invariant stochastic processes. It is a general case of the classical band-limited stochastic processes and a kind of non-band-limited stochastic processes. Two sampling theorems are obtained for the shift-invariant stochastic processes. The results for band-limited stochastic processes and shift-invariant spaces are generalized by our new results.
{"title":"Sampling and reconstruction for shift-invariant stochastic processes","authors":"Jun Xian, Song-Hua Li","doi":"10.1080/17442508.2013.763807","DOIUrl":"https://doi.org/10.1080/17442508.2013.763807","url":null,"abstract":"In this paper, combining stochastic processes with shift-invariant spaces, we introduce shift-invariant stochastic processes. It is a general case of the classical band-limited stochastic processes and a kind of non-band-limited stochastic processes. Two sampling theorems are obtained for the shift-invariant stochastic processes. The results for band-limited stochastic processes and shift-invariant spaces are generalized by our new results.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"9 1","pages":"125 - 134"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81793355","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2013.763808
P. Berti, L. Pratelli, P. Rigo
Let L be a linear space of real-bounded random variables on the probability space . A finitely additive probability P on such thatis called equivalent martingale finitely additive probability (EMFA). In this paper, EMFAs are investigated in case P0 is atomic. Existence of EMFAs is characterized and a question raised in Berti et al. (2012, J. Theoret. Probab. Available at http://economia.unipv.it/pagp/pagine_personali/prigo/arb.pdf) is answered. Some results of the following type are obtained as well. Let and Y be a bounded random variable. Then , for some sequence , provided EMFAs exist and for each EMFA P.
设L是概率空间上实有界随机变量的线性空间。这样的有限可加概率P称为等效鞅有限可加概率。本文研究了P0为原子态时的emfa。Berti et al. (2012, J. theort .)对emfa的存在进行了表征，并提出了一个问题。Probab。可在http://economia.unipv.it/pagp/pagine_personali/prigo/arb.pdf上找到)的答案。还得到了下列类型的一些结果。设Y是一个有界随机变量。然后，对于某些序列，假设存在EMFA和每个EMFA P。
{"title":"Price uniqueness and fundamental theorem of asset pricing with finitely additive probabilities","authors":"P. Berti, L. Pratelli, P. Rigo","doi":"10.1080/17442508.2013.763808","DOIUrl":"https://doi.org/10.1080/17442508.2013.763808","url":null,"abstract":"Let L be a linear space of real-bounded random variables on the probability space . A finitely additive probability P on such thatis called equivalent martingale finitely additive probability (EMFA). In this paper, EMFAs are investigated in case P0 is atomic. Existence of EMFAs is characterized and a question raised in Berti et al. (2012, J. Theoret. Probab. Available at http://economia.unipv.it/pagp/pagine_personali/prigo/arb.pdf) is answered. Some results of the following type are obtained as well. Let and Y be a bounded random variable. Then , for some sequence , provided EMFAs exist and for each EMFA P.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"37 1","pages":"135 - 146"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82188643","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}
Pub Date : 2014-01-02DOI: 10.1080/17442508.2012.749260
E. Orsingher, Bruno Toaldo
In this paper we study a class of distributions related to the r.v. , for different distributions of . The problem is related to the hitting point of a randomly oriented ray and generalizes the Cauchy distribution in different directions. We show that the distribution of solves the Laplace equation of order , possesses even moments of order , and has bimodal structure when is uniform. We study also a number of distributional properties of functionals of , including those related to the arcsine law. Finally we study the same problem in the Poincaré half-plane and this leads to the hyperbolic distribution of which the main properties are explored. In particular we study the distribution of hyperbolic functions of , the law of sums of i.i.d. r.v.'s and the distribution of the area of random hyperbolic right triangles.
{"title":"Shooting randomly against a line in Euclidean and non-Euclidean spaces","authors":"E. Orsingher, Bruno Toaldo","doi":"10.1080/17442508.2012.749260","DOIUrl":"https://doi.org/10.1080/17442508.2012.749260","url":null,"abstract":"In this paper we study a class of distributions related to the r.v. , for different distributions of . The problem is related to the hitting point of a randomly oriented ray and generalizes the Cauchy distribution in different directions. We show that the distribution of solves the Laplace equation of order , possesses even moments of order , and has bimodal structure when is uniform. We study also a number of distributional properties of functionals of , including those related to the arcsine law. Finally we study the same problem in the Poincaré half-plane and this leads to the hyperbolic distribution of which the main properties are explored. In particular we study the distribution of hyperbolic functions of , the law of sums of i.i.d. r.v.'s and the distribution of the area of random hyperbolic right triangles.","PeriodicalId":49269,"journal":{"name":"Stochastics-An International Journal of Probability and Stochastic Processes","volume":"15 1","pages":"16 - 45"},"PeriodicalIF":0.9,"publicationDate":"2014-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75984663","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}
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