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Extremes of order statistics of stationary Gaussian processes 平稳高斯过程阶统计量的极值
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.4
Chunming Zhao
{"title":"Extremes of order statistics of stationary Gaussian processes","authors":"Chunming Zhao","doi":"10.19195/0208-4147.38.1.4","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.4","url":null,"abstract":"Tu wpisz tekst","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46051840","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: 3
Sharp bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units 以基尼均差单位表示的第k个记录的线性组合的期望值的锐界
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.3
P. Kozyra, T. Rychlik
{"title":"Sharp bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units","authors":"P. Kozyra, T. Rychlik","doi":"10.19195/0208-4147.38.1.3","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.3","url":null,"abstract":"We describe a method of calculating sharp lower and upper bounds on the expectations of linear combinations of kth records expressed in the Gini mean difference units of the original i.i.d. observations. In particular, we provide sharp lower and upper bounds on the expectations of kth records and their differences. We also present the families of distributions which attain the bounds in the limit.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44181348","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: 5
Bellman equations for terminal utility maximization with general bid and ask prices 具有一般买卖价格的终端效用最大化的贝尔曼方程
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.8
T. Rogala, Ł. Stettner
{"title":"Bellman equations for terminal utility maximization with general bid and ask prices","authors":"T. Rogala, Ł. Stettner","doi":"10.19195/0208-4147.38.1.8","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.8","url":null,"abstract":"In the paper we solve a system of Bellman equations for finite horizon continuous time terminal utility maximization problem with general càdlàg bid and ask prices. We assume that we have a restricted number of transactions at time moments we choose. The main result of the paper says that we can find a regular version of solutions to the system of Bellman equations, which enables us to find the form of nearly optimal strategies.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41704667","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
Stationarity against integration in the autoregressive process with polynomial trend 多项式趋势自回归过程的抗积分平稳性
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.1
F. Proïa
{"title":"Stationarity against integration in the autoregressive process with polynomial trend","authors":"F. Proïa","doi":"10.19195/0208-4147.38.1.1","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.1","url":null,"abstract":"We tackle the stationarity issue of an autoregressive path with a polynomial trend, and generalize some aspects of the LMC test, the testing procedure of Leybourne and McCabe. First, we show that it is possible to get the asymptotic distribution of the test statistic under the null hypothesis of trend-stationarity as well as under the alternative of nonstationarity for any polynomial trend of order r. Then, we explain the reason why the LMC test, and by extension the KPSS test, does not reject the null hypothesis of trend-stationarity, mistakenly, when the random walk is generated by a unit root located at −1.We also observe it on simulated data and correct the procedure. Finally, we describe some useful stochastic processes that appear in our limiting distributions.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45774118","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
A reverse to the Jeffreys–Lindley paradox 杰弗里斯-林德利悖论的反面
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.13
W. Pestman, F. Tuerlinckx, W. Vanpaemel
{"title":"A reverse to the Jeffreys–Lindley paradox","authors":"W. Pestman, F. Tuerlinckx, W. Vanpaemel","doi":"10.19195/0208-4147.38.1.13","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.13","url":null,"abstract":"In this paper the seminal Jeffreys–Lindley paradox is regarded from a mathematical point of view. We show that in certain scenarios the paradox may emerge in a reverse direction.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42934716","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
A consistent estimator for spectral density matrix of a discrete time periodically correlated process 离散时间周期相关过程谱密度矩阵的一致估计
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-07-30 DOI: 10.19195/0208-4147.38.1.12
M. Azimmohseni, A. Soltani, M. Khalafi, Naeemeh Akbari Ghalesary
{"title":"A consistent estimator for spectral density matrix of a discrete time periodically correlated process","authors":"M. Azimmohseni, A. Soltani, M. Khalafi, Naeemeh Akbari Ghalesary","doi":"10.19195/0208-4147.38.1.12","DOIUrl":"https://doi.org/10.19195/0208-4147.38.1.12","url":null,"abstract":"In this article, we introduce a weighted periodogram in the class of smoothed periodograms as a consistent estimator for the spectral density matrix of a periodically correlated process. We derive its limiting distribution that appears to be a certain finite linear combination of Wishart distribution. We also provide numerical derivations for our smoothed periodogram and exhibit its asymptotic consistency using simulated data.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41615531","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
On Mixtures of Gamma distributions, distributions with hyperbolically monotone densities and Generalized Gamma Convolutions (GGC) 关于伽玛分布、双曲单调密度分布和广义伽玛卷积的混合
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-06-11 DOI: 10.37190/0208-4147.41.1.1
Tord Sjödin
{"title":"On Mixtures of Gamma distributions, distributions with hyperbolically monotone densities and Generalized Gamma Convolutions (GGC)","authors":"Tord Sjödin","doi":"10.37190/0208-4147.41.1.1","DOIUrl":"https://doi.org/10.37190/0208-4147.41.1.1","url":null,"abstract":"Let $Y$ be a standard Gamma(k) distributed random variable, $k>0$, and let $X$ be an independent positive random variable. We prove that if $X$ has a hyperbolically monotone density of order $k$ ($HM_k$), then the distributions of $Ycdot X$ and $Y/X$ are generalized gamma convolutions (GGC). This result extends results of Roynette et al. and Behme and Bondesson, who treated respectively the cases $k=1$ and $k$ an integer. We give a proof that covers all $k>0$ and gives explicit formulas for the relevant functions that extend those found by Behme and Bondesson in the integer case.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44013372","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
Estimates of the transition densities for the reflected Brownian motion on simple nested fractals 简单嵌套分形上反射布朗运动的跃迁密度估计
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-04-13 DOI: 10.19195/0208-4147.39.2.10
M. Olszewski
{"title":"Estimates of the transition densities for the reflected Brownian motion on simple nested fractals","authors":"M. Olszewski","doi":"10.19195/0208-4147.39.2.10","DOIUrl":"https://doi.org/10.19195/0208-4147.39.2.10","url":null,"abstract":"We give sharp two-sided estimates for the functions gMt, x, y and gMt, x, y − gt, x, y, where gMt, x, y are the transition probability densities of the reflected Brownian motion on an Mcomplex of order M ∈ Z of an unbounded planar simple nested fractal and gt, x, y are the transition probability densities of the “free” Brownian motion on this fractal. This is done for a large class of planar simple nested fractals with the good labeling property.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42689555","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: 4
On tails of symmetric and totally asymmetric alpha-stable distributions 对称和完全不对称稳定分布的尾部
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2018-02-02 DOI: 10.37190/0208-4147.41.2.7
W. Bednorz, R. Lochowski, Rafał Martynek
{"title":"On tails of symmetric and totally asymmetric alpha-stable distributions","authors":"W. Bednorz, R. Lochowski, Rafał Martynek","doi":"10.37190/0208-4147.41.2.7","DOIUrl":"https://doi.org/10.37190/0208-4147.41.2.7","url":null,"abstract":"We estimate up to universal constants tails of symmetric and totally asymmetric $alpha$-stable distributions in terms of functions of the parameters of these distributions.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46848842","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
Regularly log-periodic functions and some applications 有规律的对数周期函数和一些应用
IF 0.3 4区 数学
Probability and Mathematical Statistics-Poland Pub Date : 2017-09-06 DOI: 10.37190/0208-4147.40.1.10
P. Kevei
{"title":"Regularly log-periodic functions and some applications","authors":"P. Kevei","doi":"10.37190/0208-4147.40.1.10","DOIUrl":"https://doi.org/10.37190/0208-4147.40.1.10","url":null,"abstract":"We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type smoothing transforms.","PeriodicalId":48996,"journal":{"name":"Probability and Mathematical Statistics-Poland","volume":null,"pages":null},"PeriodicalIF":0.3,"publicationDate":"2017-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48967531","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
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